From 81614c2678c2605dfe68ea2b1fbbcf6b86270ba0 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 28 Oct 2023 04:00:16 +0000 Subject: [PATCH] build based on 0fd6134 --- stable | 2 +- v2 | 2 +- v2.5 | 1 + v2.5.0/.documenter-siteinfo.json | 1 + v2.5.0/api/index.html | 78 ++ v2.5.0/assets/documenter.js | 889 ++++++++++++++++++++++ v2.5.0/assets/logo.svg | 8 + v2.5.0/assets/themes/documenter-dark.css | 7 + v2.5.0/assets/themes/documenter-light.css | 9 + v2.5.0/assets/themeswap.js | 84 ++ v2.5.0/assets/warner.js | 52 ++ v2.5.0/index.html | 120 +++ v2.5.0/search_index.js | 3 + v2.5.0/siteinfo.js | 1 + versions.js | 3 +- 15 files changed, 1257 insertions(+), 3 deletions(-) create mode 120000 v2.5 create mode 100644 v2.5.0/.documenter-siteinfo.json create mode 100644 v2.5.0/api/index.html create mode 100644 v2.5.0/assets/documenter.js create mode 100644 v2.5.0/assets/logo.svg create mode 100644 v2.5.0/assets/themes/documenter-dark.css create mode 100644 v2.5.0/assets/themes/documenter-light.css create mode 100644 v2.5.0/assets/themeswap.js create mode 100644 v2.5.0/assets/warner.js create mode 100644 v2.5.0/index.html create mode 100644 v2.5.0/search_index.js create mode 100644 v2.5.0/siteinfo.js diff --git a/stable b/stable index fa49670..d80b4a8 120000 --- a/stable +++ b/stable @@ -1 +1 @@ -v2.4.0 \ No newline at end of file +v2.5.0 \ No newline at end of file diff --git a/v2 b/v2 index fa49670..d80b4a8 120000 --- a/v2 +++ b/v2 @@ -1 +1 @@ -v2.4.0 \ No newline at end of file +v2.5.0 \ No newline at end of file diff --git a/v2.5 b/v2.5 new file mode 120000 index 0000000..d80b4a8 --- /dev/null +++ b/v2.5 @@ -0,0 +1 @@ +v2.5.0 \ No newline at end of file diff --git a/v2.5.0/.documenter-siteinfo.json b/v2.5.0/.documenter-siteinfo.json new file mode 100644 index 0000000..613cc93 --- /dev/null +++ b/v2.5.0/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2023-10-28T04:00:10","documenter_version":"1.1.2"}} \ No newline at end of file diff --git a/v2.5.0/api/index.html b/v2.5.0/api/index.html new file mode 100644 index 0000000..ee952bd --- /dev/null +++ b/v2.5.0/api/index.html @@ -0,0 +1,78 @@ + +API Reference · LifeContingencies.jl

LifeContingencies API Reference

Exported API

LifeContingencies.InsuranceMethod
Insurance(lc::LifeContingency, term)
+Insurance(life,interest, term)
+Insurance(lc::LifeContingency)
+Insurance(life,interest)

Life insurance with a term period of term. If term is nothing, then whole life insurance.

Issue age is based on the issue_age in the LifeContingency lc.

Examples

ins = Insurance(
+    SingleLife(mortality = UltimateMortality([0.5,0.5]),issue_age = 0),
+    FinanceModels.Yield.Constant(0.05),
+    1           # 1 year term
+) 
source
LifeContingencies.JointLifeType
struct JointLife
+    lives
+    contingency
+    joint_assumption
+end
+
+A `Life` object containing the necessary assumptions for contingent maths related to a joint life insurance. Use with a `LifeContingency` to do many actuarial present value calculations.

Keyword arguments:

  • lives is a tuple of two SingleLifes
  • contingency default is LastSurvivor(). It is the trigger for contingent benefits. See ?Contingency.
  • joint_assumption Default value is Frasier(). It is the assumed relationship between the mortality of the two lives. See ?JointAssumption.

Examples

using MortalityTables
+mortality = MortalityTables.table("2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB")
+
+l1 = SingleLife(
+    mortality       = mortality.select[30], 
+    issue_age  = 30          
+)
+l2 = SingleLife(
+    mortality       = mortality.select[30], 
+    issue_age  = 30          
+)
+
+jl = JointLife(
+    lives = (l1,l2),
+    contingency = LastSurvivor(),
+    joint_assumption = Frasier()
+)
source
LifeContingencies.SingleLifeType
struct SingleLife
+    mortality
+    issue_age::Int
+    alive::Bool
+    fractional_assump::MortalityTables.DeathDistribution
+end

A Life object containing the necessary assumptions for contingent maths related to a single life. Use with a LifeContingency to do many actuarial present value calculations.

Keyword arguments:

  • mortality pass a mortality vector, which is an array of applicable mortality rates indexed by attained age
  • issue_age is the assumed issue age for the SingleLife and is the basis of many contingency calculations.
  • alive Default value is true. Useful for joint insurances with different status on the lives insured.
  • fractional_assump. Default value is Uniform(). This is a DeathDistribution from the MortalityTables.jl package and is the assumption to use for non-integer ages/times.

Examples

using MortalityTables
+mortality = MortalityTables.table("2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB")
+
+SingleLife(
+    mort       = mort.select[30], 
+    issue_age  = 30          
+)
source
FinanceCore.discountMethod
discount(Insurance)

The discount vector for the given insurance.

To get the fully computed and allocated vector, call collect(discount(...)).

source
FinanceCore.present_valueMethod
present_value(Insurance,`time`)

The actuarial present value of the given insurance benefits, as if you were standing at time.

For example, if the given Insurance has decremented payments [1,2,3,4,5] at times [1,2,3,4,5] and you call pv(ins,3), you will get the present value of the payments [4,5] at times [1,2].

To get an undecremented present value, divide by the survivorship to that timepoint:

present_value(ins,10) / survival(ins,10)
source
LifeContingencies.APVMethod
APV(lc::LifeContingency,to_time)

The actuarial present value which is the survival times the discount factor for the life contingency.

source
LifeContingencies.AnnuityDueMethod
AnnuityDue(lc::LifeContingency; n=nothing, start_time=0; certain=nothing,frequency=1)
+AnnuityDue(life, interest; n=nothing, start_time=0; certain=nothing,frequency=1)

Annuity due with the benefit period starting at start_time and ending after n periods with frequency payments per year of 1/frequency amount and a certain period with non-contingent payments.

Examples

ins = AnnuityDue(
+    SingleLife(mortality = UltimateMortality([0.5,0.5]),issue_age = 0),
+    FinanceModels.Yield.Constant(0.05),
+    1, # term of policy
+) 
source
LifeContingencies.AnnuityImmediateMethod
AnnuityImmediate(lc::LifeContingency; term=nothing, start_time=0; certain=nothing,frequency=1)
+AnnuityImmediate(life, interest; term=nothing, start_time=0; certain=nothing,frequency=1)

Annuity immediate with the benefit period starting at start_time and ending after term periods with frequency payments per year of 1/frequency amount and a certain period with non-contingent payments.

Examples

ins = AnnuityImmediate(
+    SingleLife(mortality = UltimateMortality([0.5,0.5]),issue_age = 0),
+    FinanceModels.Yield.Constant(0.05),
+    1 # term of policy
+) 
source
LifeContingencies.cashflowsMethod
cashflows(Insurance)

The vector of decremented benefit cashflows for the given insurance.

To get the fully computed and allocated vector, call collect(cashflows(...)).

source
LifeContingencies.premium_netMethod
premium_net(lc::LifeContingency)
+premium_net(lc::LifeContingency,to_time)

The net premium for a whole life insurance (without second argument) or a term life insurance through to_time.

The net premium is based on 1 unit of insurance with the death benfit payable at the end of the year and assuming annual net premiums.

source
LifeContingencies.probabilityMethod
probability(Insurance)

The vector of contingent benefit probabilities for the given insurance.

To get the fully computed and allocated vector, call collect(probability(...)).

source
LifeContingencies.timepointsMethod
timepoints(Insurance)

The vector of times corresponding to the cashflow vector for the given insurance.

To get the fully computed and allocated vector, call collect(timepoints(...)).

source
MortalityTables.omegaMethod
omega(lc::LifeContingency)
+omega(l::Life)
+omega(i::InterestRate)

Lifes and LifeContingencys

Returns the last defined timeperiod for both the interest rate and mortality table. Note that this is different than calling omega on a MortalityTable, which will give you the last `attainedage`.

Example: if the LifeContingency has issue age 60, and the last defined attained age for the MortalityTable is 100, then omega of the MortalityTable will be 100 and omega of the LifeContingency will be 40.

InterestRates

The last period that the interest rate is defined for. Assumed to be infinite (Inf) for functional and constant interest rate types. Returns the lastindex of the vector if a vector type.

source
MortalityTables.survivalMethod
survival(Insurance)

The survivorship vector for the given insurance.

To get the fully computed and allocated vector, call collect(survival(...)).

source
MortalityTables.survivalMethod
survival(lc::LifeContingency,from_time,to_time)
+survival(lc::LifeContingency,to_time)

Return the probability of survival for the given LifeContingency, with decrements beginning at time zero.

Examples

```julia-repl julia> q = [.1,.2,.3,.4];

julia> l = SingleLife(mortality=q);

julia> survival(l,1) 0.9

julia> decrement(l,1) 0.09999999999999998

julia> survival(l,1,2) 0.8

julia> decrement(l,1,2) 0.19999999999999996

julia> survival(l,1,3) 0.5599999999999999

julia> decrement(l,1,3) 0.44000000000000006

```
source

Unexported API

LifeContingencies.ContingencyType
Contingency()

An abstract type representing the different triggers for contingent benefits. Available options to use include:

  • LastSurvivor()
source
LifeContingencies.JointAssumptionType
JointAssumption()

An abstract type representing the different assumed relationship between the survival of the lives on a JointLife. Available options to use include:

  • Frasier()
source
LifeContingencies.CMethod
C(lc::LifeContingency, to_time)

$C_x$ is a retrospective actuarial commutation function which is the product of the discount factor and the difference in l ($l_x$).

source
LifeContingencies.DMethod
D(lc::LifeContingency, to_time)

$D_x$ is a retrospective actuarial commutation function which is the product of the survival and discount factor.

source
LifeContingencies.MMethod
M(lc::LifeContingency, from_time)

The $M_x$ actuarial commutation function where the from_time argument is x. Issue age is based on the issue_age in the LifeContingency lc.

source
LifeContingencies.NMethod
N(lc::LifeContingency, from_time)

$N_x$ is a prospective actuarial commutation function which is the sum of the D ($D_x$) values from the given time to the end of the mortality table.

source
LifeContingencies.lMethod
l(lc::LifeContingency, to_time)

$l_x$ is a retrospective actuarial commutation function which is the survival up to a certain point in time. By default, will have a unitary basis (ie 1.0), but you can specify basis keyword argument to use something different (e.g. 1000 is common in the literature.)

source
MortalityTables.decrementMethod
decrement(lc::LifeContingency,to_time)
+decrement(lc::LifeContingency,from_time,to_time)

Return the probability of death for the given LifeContingency, with decrements beginning at time zero.

Examples

julia> q = [.1,.2,.3,.4];
+
+julia> l = SingleLife(mortality=q);
+
+julia> survival(l,1)
+0.9
+
+julia> decrement(l,1)
+0.09999999999999998
+
+julia> survival(l,1,2)
+0.8
+
+julia> decrement(l,1,2)
+0.19999999999999996
+
+julia> survival(l,1,3)
+0.5599999999999999
+
+julia> decrement(l,1,3)
+0.44000000000000006
source

Please open an issue if you encounter any issues or confusion with the package.

diff --git a/v2.5.0/assets/documenter.js b/v2.5.0/assets/documenter.js new file mode 100644 index 0000000..f531160 --- /dev/null +++ b/v2.5.0/assets/documenter.js @@ -0,0 +1,889 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+
+ ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` + +`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v2.5.0/assets/logo.svg b/v2.5.0/assets/logo.svg new file mode 100644 index 0000000..aa20747 --- /dev/null +++ b/v2.5.0/assets/logo.svg @@ -0,0 +1,8 @@ + + + + + + + + \ No newline at end of file diff --git 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kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content 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html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark 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.button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#024c7d}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #024c7d #024c7d !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-info.is-light{background-color:#ebf7ff;color:#0e9dfb}html.theme--documenter-dark .button.is-info.is-light:hover,html.theme--documenter-dark .button.is-info.is-light.is-hovered{background-color:#def2fe;border-color:transparent;color:#0e9dfb}html.theme--documenter-dark .button.is-info.is-light:active,html.theme--documenter-dark .button.is-info.is-light.is-active{background-color:#d2edfe;border-color:transparent;color:#0e9dfb}html.theme--documenter-dark .button.is-success{background-color:#008438;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:hover,html.theme--documenter-dark .button.is-success.is-hovered{background-color:#073;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus,html.theme--documenter-dark 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.button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#008438;box-shadow:none;color:#008438}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#008438}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #008438 #008438 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success.is-light{background-color:#ebfff3;color:#00eb64}html.theme--documenter-dark .button.is-success.is-light:hover,html.theme--documenter-dark 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.button.is-warning.is-active{background-color:#946e00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:#ad8100;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-outlined.is-focused{background-color:#ad8100;border-color:#ad8100;color:#fff}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark 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.button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#92190c;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(158,27,13,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#86170b;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:#9e1b0d;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark 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.docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--documenter-dark .image.is-1by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--documenter-dark .image.is-16x16,html.theme--documenter-dark #documenter .docs-sidebar 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LifeContingencies.jl

Stable Dev codecov

LifeContingencies is a package enabling actuarial life contingent calculations.

Features

  • Integration with other JuliaActuary packages such as MortalityTables.jl
  • Fast calculations, with some parts utilizing parallel processing power automatically
  • Use functions that look more like the math you are used to (e.g. A, ) with Unicode support
  • All of the power, speed, convenience, tooling, and ecosystem of Julia
  • Flexible and modular modeling approach

Package Overview

the mortality calculations

  • Contains common insurance calculations such as:
    • Insurance(life,yield): Whole life
    • Insurance(life,yield,n): Term life for n years
    • ä(life,yield): present_value of life-contingent annuity
    • ä(life,yield,n): present_value of life-contingent annuity due for n years
  • Contains various commutation functions such as D(x),M(x),C(x), etc.
  • SingleLife and JointLife capable
  • Interest rate mechanics via Yields.jl
  • More documentation available by clicking the DOCS badges at the top of this README

Examples

Basic Functions

Calculate various items for a 30-year-old male nonsmoker using 2015 VBT base table and a 5% interest rate


+using LifeContingencies
+using MortalityTables
+using Yields
+import LifeContingencies: V, ä     # pull the shortform notation into scope
+
+# load mortality rates from MortalityTables.jl
+vbt2001 = MortalityTables.table("2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB")
+
+issue_age = 30
+life = SingleLife(                 # The life underlying the risk
+    mort = vbt2001.select[issue_age],    # -- Mortality rates
+)
+
+yield = Yields.Constant(0.05)      # Using a flat 5% interest rate
+
+lc = LifeContingency(life, yield)  # LifeContingency joins the risk with interest
+
+
+ins = Insurance(lc)                # Whole Life insurance
+ins = Insurance(life, yield)       # alternate way to construct

With the above life contingent data, we can calculate vectors of relevant information:

cashflows(ins)                     # A vector of the unit cashflows
+timepoints(ins)                    # The timepoints associated with the cashflows
+survival(ins)                      # The survival vector
+survival(ins,time)                 # The survivorship through `time`
+benefit(ins)                       # The unit benefit vector
+probability(ins)                   # The probability of benefit payment
+present_value(ins)                 # the present value of the insurance benefits from time zero
+present_value(ins,time)            # the present value of the insurance benefits from `time`

Some of the above will return lazy results. For example, cashflows(ins) will return a Generator which can be efficiently used in most places you'd use a vector of cashflows (e.g. pv(...) or sum(...)) but has the advantage of being non-allocating (less memory used, faster computations). To get a computed vector instead of the generator, simply call collect(...) on the result: collect(cashflows(ins)).

Or calculate summary scalars:

present_value(ins)                 # The actuarial present value
+premium_net(lc)                    # Net whole life premium 
+V(lc,5)                            # Net premium reserve for whole life insurance at time 5

Other types of life contingent benefits:

Insurance(lc,10)                 # 10 year term insurance
+AnnuityImmediate(lc)               # Whole life annuity due
+AnnuityDue(lc)                     # Whole life annuity due
+ä(lc)                              # Shortform notation
+ä(lc, 5)                           # 5 year annuity due
+ä(lc, 5, certain=5,frequency=4)    # 5 year annuity due, with 5 year certain payable 4x per year
+...                                # and more!

Constructing Lives

SingleLife(vbt2001.select[50])                 # no keywords, just a mortality vector
+SingleLife(vbt2001.select[50],issue_age = 60)  # select at 50, but now 60
+SingleLife(vbt2001.select,issue_age = 50)      # use issue_age to pick the right select vector
+SingleLife(mortality=vbt2001.select,issue_age = 50) # mort can also be a keyword
+

Net Premium for Term Policy with Stochastic rates

Use a stochastic interest rate calculation to price a term policy:

using LifeContingencies, MortalityTables
+using Distributions
+
+vbt2001 = MortalityTables.table("2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB")
+
+# use an interest rate that's normally distirbuted
+μ = 0.05
+σ = 0.01
+
+years = 100
+int =   Yields.Forward(rand(Normal(μ,σ), years))
+
+life = SingleLife(mortality = vbt2001.select[30], issue_age = 30)
+
+term = 10
+LifeContingencies.A(lc, term) # around 0.055

Extending example to use autocorrelated interest rates

You can use autocorrelated interest rates - substitute the following in the prior example using the ability to self reference:

σ = 0.01
+initial_rate = 0.05
+vec = fill(initial_rate, years)
+
+for i in 2:length(vec)
+    vec[i] = rand(Normal(vec[i-1], σ))
+end
+
+int = Yields.Forward(vec)

Premium comparison across Mortality Tables

Compare the cost of annual premium, whole life insurance between multiple tables visually:

using LifeContingencies, MortalityTables, Plots
+
+tables = [
+    MortalityTables.table("1980 CET - Male Nonsmoker, ANB"),
+    MortalityTables.table("2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB"),
+    MortalityTables.table("2015 VBT Male Non-Smoker RR100 ANB"),
+    ]
+
+issue_ages = 30:90
+int = Yields.Constant(0.05)
+
+whole_life_costs = map(tables) do t
+    map(issue_ages) do ia
+        lc = LifeContingency(SingleLife(mortality = t.ultimate, issue_age = ia), int)
+        premium_net(lc)
+
+    end
+end
+
+plt = plot(ylabel="Annual Premium per unit", xlabel="Issue Age",
+           legend=:topleft, legendfontsize=8,size=(800,600))
+
+for (i,t) in enumerate(tables)
+    plot!(plt,issue_ages,whole_life_costs[i], label="$(t.metadata.name)")
+end
+
+display(plt)

Comparison of three different mortality tables' effect on insurance cost

Joint Life

m1 = MortalityTables.table("1986-92 CIA – Male Smoker, ANB")
+m2 = MortalityTables.table("1986-92 CIA – Female Nonsmoker, ANB")
+l1 = SingleLife(mortality = m1.ultimate, issue_age = 40)
+l2 = SingleLife(mortality = m2.ultimate, issue_age = 37)
+
+jl = JointLife(lives=(l1, l2), contingency=LastSurvivor(), joint_assumption=Frasier())
+
+
+Insurance(jl,Yields.Constant(0.05))      # whole life insurance
+...                                      # similar functions as shown in the first example above

Commutation and Unexported Function shorthand

Because it's so common to use certain variables in your own code, LifeContingencies avoids exporting certain variables/functions so that it doesn't collide with your own usage. For example, you may find yourself doing something like:

a = ...
+b = ...
+result = b - a

If you imported using LifeContingencies and the package exported a (annuity_immediate) then you could have problems if you tried to do the above. To avoid this, we only export long-form functions like annuity_immediate. To utilize the shorthand, you can include them into your code's scope like so:

using LifeContingencies # brings all the default functions into your scope
+using LifeContingencies: a, ä # also brings the short-form annuity functions into scope

Or you can do the following:

using LifeContingencies # brings all the default functions into your scope
+... # later on in the code
+LifeContingencies.ä(...) # utilize the unexported function with the module name

For more on module scoping, see the Julia Manual section.

Actuarial notation shorthand

V => reserve_premium_net
+v => discount
+A => present value of Insurance
+ä => present value of AnnuityDue
+a => present value of AnnuityImmediate
+P => premium_net
+ω => omega

Commutation functions

l,
+D,
+M,
+N,
+C,

References

+
diff --git a/v2.5.0/search_index.js b/v2.5.0/search_index.js new file mode 100644 index 0000000..84321c0 --- /dev/null +++ b/v2.5.0/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#LifeContingencies-API-Reference","page":"API Reference","title":"LifeContingencies API Reference","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Modules = [LifeContingencies]","category":"page"},{"location":"api/#Exported-API","page":"API Reference","title":"Exported API","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Modules = [LifeContingencies]\nPrivate = false","category":"page"},{"location":"api/#LifeContingencies.Frasier","page":"API Reference","title":"LifeContingencies.Frasier","text":"Frasier()\n\nThe assumption of independent lives in a joint life calculation. Is a subtype of JointAssumption.\n\n\n\n\n\n","category":"type"},{"location":"api/#LifeContingencies.Insurance-Tuple{LifeContingency, Any}","page":"API Reference","title":"LifeContingencies.Insurance","text":"Insurance(lc::LifeContingency, term)\nInsurance(life,interest, term)\nInsurance(lc::LifeContingency)\nInsurance(life,interest)\n\nLife insurance with a term period of term. If term is nothing, then whole life insurance.\n\nIssue age is based on the issue_age in the LifeContingency lc.\n\nExamples\n\nins = Insurance(\n SingleLife(mortality = UltimateMortality([0.5,0.5]),issue_age = 0),\n FinanceModels.Yield.Constant(0.05),\n 1 # 1 year term\n) \n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.JointLife","page":"API Reference","title":"LifeContingencies.JointLife","text":"struct JointLife\n lives\n contingency\n joint_assumption\nend\n\nA `Life` object containing the necessary assumptions for contingent maths related to a joint life insurance. Use with a `LifeContingency` to do many actuarial present value calculations.\n\nKeyword arguments:\n\nlives is a tuple of two SingleLifes\ncontingency default is LastSurvivor(). It is the trigger for contingent benefits. See ?Contingency. \njoint_assumption Default value is Frasier(). It is the assumed relationship between the mortality of the two lives. See ?JointAssumption. \n\nExamples\n\nusing MortalityTables\nmortality = MortalityTables.table(\"2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB\")\n\nl1 = SingleLife(\n mortality = mortality.select[30], \n issue_age = 30 \n)\nl2 = SingleLife(\n mortality = mortality.select[30], \n issue_age = 30 \n)\n\njl = JointLife(\n lives = (l1,l2),\n contingency = LastSurvivor(),\n joint_assumption = Frasier()\n)\n\n\n\n\n\n","category":"type"},{"location":"api/#LifeContingencies.LastSurvivor","page":"API Reference","title":"LifeContingencies.LastSurvivor","text":"LastSurvivor()\n\nThe contingency whereupon benefits are payable upon both lives passing. Is a subtype of Contingency\n\n\n\n\n\n","category":"type"},{"location":"api/#LifeContingencies.LifeContingency","page":"API Reference","title":"LifeContingencies.LifeContingency","text":"struct LifeContingency\n life::Life\n\n\n\n\n\n","category":"type"},{"location":"api/#LifeContingencies.SingleLife","page":"API Reference","title":"LifeContingencies.SingleLife","text":"struct SingleLife\n mortality\n issue_age::Int\n alive::Bool\n fractional_assump::MortalityTables.DeathDistribution\nend\n\nA Life object containing the necessary assumptions for contingent maths related to a single life. Use with a LifeContingency to do many actuarial present value calculations. \n\nKeyword arguments:\n\nmortality pass a mortality vector, which is an array of applicable mortality rates indexed by attained age\nissue_age is the assumed issue age for the SingleLife and is the basis of many contingency calculations.\nalive Default value is true. Useful for joint insurances with different status on the lives insured.\nfractional_assump. Default value is Uniform(). This is a DeathDistribution from the MortalityTables.jl package and is the assumption to use for non-integer ages/times.\n\nExamples\n\nusing MortalityTables\nmortality = MortalityTables.table(\"2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB\")\n\nSingleLife(\n mort = mort.select[30], \n issue_age = 30 \n)\n\n\n\n\n\n","category":"type"},{"location":"api/#FinanceCore.discount-Tuple{I} where I<:Insurance","page":"API Reference","title":"FinanceCore.discount","text":"discount(Insurance)\n\nThe discount vector for the given insurance.\n\nTo get the fully computed and allocated vector, call collect(discount(...)).\n\n\n\n\n\n","category":"method"},{"location":"api/#FinanceCore.present_value-Tuple{T} where T<:Insurance","page":"API Reference","title":"FinanceCore.present_value","text":"present_value(Insurance)\n\nThe actuarial present value of the given insurance benefits.\n\n\n\n\n\n","category":"method"},{"location":"api/#FinanceCore.present_value-Union{Tuple{T}, Tuple{T, Any}} where T<:Insurance","page":"API Reference","title":"FinanceCore.present_value","text":"present_value(Insurance,`time`)\n\nThe actuarial present value of the given insurance benefits, as if you were standing at time. \n\nFor example, if the given Insurance has decremented payments [1,2,3,4,5] at times [1,2,3,4,5] and you call pv(ins,3), you will get the present value of the payments [4,5] at times [1,2].\n\nTo get an undecremented present value, divide by the survivorship to that timepoint:\n\npresent_value(ins,10) / survival(ins,10)\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.APV-Tuple{LifeContingency, Any}","page":"API Reference","title":"LifeContingencies.APV","text":"APV(lc::LifeContingency,to_time)\n\nThe actuarial present value which is the survival times the discount factor for the life contingency.\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.AnnuityDue-Tuple{Any, Any, Any}","page":"API Reference","title":"LifeContingencies.AnnuityDue","text":"AnnuityDue(lc::LifeContingency; n=nothing, start_time=0; certain=nothing,frequency=1)\nAnnuityDue(life, interest; n=nothing, start_time=0; certain=nothing,frequency=1)\n\nAnnuity due with the benefit period starting at start_time and ending after n periods with frequency payments per year of 1/frequency amount and a certain period with non-contingent payments. \n\nExamples\n\nins = AnnuityDue(\n SingleLife(mortality = UltimateMortality([0.5,0.5]),issue_age = 0),\n FinanceModels.Yield.Constant(0.05),\n 1, # term of policy\n) \n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.AnnuityImmediate-Tuple{Any, Any, Any}","page":"API Reference","title":"LifeContingencies.AnnuityImmediate","text":"AnnuityImmediate(lc::LifeContingency; term=nothing, start_time=0; certain=nothing,frequency=1)\nAnnuityImmediate(life, interest; term=nothing, start_time=0; certain=nothing,frequency=1)\n\nAnnuity immediate with the benefit period starting at start_time and ending after term periods with frequency payments per year of 1/frequency amount and a certain period with non-contingent payments. \n\nExamples\n\nins = AnnuityImmediate(\n SingleLife(mortality = UltimateMortality([0.5,0.5]),issue_age = 0),\n FinanceModels.Yield.Constant(0.05),\n 1 # term of policy\n) \n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.benefit-Tuple{I} where I<:Insurance","page":"API Reference","title":"LifeContingencies.benefit","text":"benefit(Insurance)\n\nThe unit benefit for the given insurance.\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.cashflows-Tuple{I} where I<:Insurance","page":"API Reference","title":"LifeContingencies.cashflows","text":"cashflows(Insurance)\n\nThe vector of decremented benefit cashflows for the given insurance. \n\nTo get the fully computed and allocated vector, call collect(cashflows(...)).\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.premium_net-Tuple{LifeContingency}","page":"API Reference","title":"LifeContingencies.premium_net","text":"premium_net(lc::LifeContingency)\npremium_net(lc::LifeContingency,to_time)\n\nThe net premium for a whole life insurance (without second argument) or a term life insurance through to_time.\n\nThe net premium is based on 1 unit of insurance with the death benfit payable at the end of the year and assuming annual net premiums.\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.probability-Tuple{I} where I<:Insurance","page":"API Reference","title":"LifeContingencies.probability","text":"probability(Insurance)\n\nThe vector of contingent benefit probabilities for the given insurance.\n\nTo get the fully computed and allocated vector, call collect(probability(...)).\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.reserve_premium_net-Tuple{LifeContingency, Any}","page":"API Reference","title":"LifeContingencies.reserve_premium_net","text":" reserve_premium_net(lc::LifeContingency,time)\n\nThe net premium reserve at the end of year time.\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.timepoints-Tuple{Insurance}","page":"API Reference","title":"LifeContingencies.timepoints","text":"timepoints(Insurance)\n\nThe vector of times corresponding to the cashflow vector for the given insurance.\n\nTo get the fully computed and allocated vector, call collect(timepoints(...)).\n\n\n\n\n\n","category":"method"},{"location":"api/#MortalityTables.omega-Tuple{LifeContingency}","page":"API Reference","title":"MortalityTables.omega","text":"omega(lc::LifeContingency)\nomega(l::Life)\nomega(i::InterestRate)\n\nLifes and LifeContingencys\n\nReturns the last defined timeperiod for both the interest rate and mortality table. Note that this is different than calling omega on a MortalityTable, which will give you the last `attainedage`.\n\nExample: if the LifeContingency has issue age 60, and the last defined attained age for the MortalityTable is 100, then omega of the MortalityTable will be 100 and omega of the LifeContingency will be 40.\n\nInterestRates\n\nThe last period that the interest rate is defined for. Assumed to be infinite (Inf) for functional and constant interest rate types. Returns the lastindex of the vector if a vector type.\n\n\n\n\n\n","category":"method"},{"location":"api/#MortalityTables.survival-Tuple{I} where I<:Insurance","page":"API Reference","title":"MortalityTables.survival","text":"survival(Insurance)\n\nThe survivorship vector for the given insurance.\n\nTo get the fully computed and allocated vector, call collect(survival(...)).\n\n\n\n\n\n","category":"method"},{"location":"api/#MortalityTables.survival-Tuple{LifeContingency, Any}","page":"API Reference","title":"MortalityTables.survival","text":"survival(lc::LifeContingency,from_time,to_time)\nsurvival(lc::LifeContingency,to_time)\n\nReturn the probability of survival for the given LifeContingency, with decrements beginning at time zero. \n\nExamples\n\n```julia-repl julia> q = [.1,.2,.3,.4];\n\njulia> l = SingleLife(mortality=q);\n\njulia> survival(l,1) 0.9\n\njulia> decrement(l,1) 0.09999999999999998\n\njulia> survival(l,1,2) 0.8\n\njulia> decrement(l,1,2) 0.19999999999999996\n\njulia> survival(l,1,3) 0.5599999999999999\n\njulia> decrement(l,1,3) 0.44000000000000006\n\n```\n\n\n\n\n\n","category":"method"},{"location":"api/#MortalityTables.survival-Tuple{L} where L<:LifeContingencies.Life","page":"API Reference","title":"MortalityTables.survival","text":"survival(life)\n\nReturn a survival vector for the given life.\n\n\n\n\n\n","category":"method"},{"location":"api/#MortalityTables.survival-Union{Tuple{I}, Tuple{I, Any}} where I<:Insurance","page":"API Reference","title":"MortalityTables.survival","text":"survival(Insurance,time)\n\nThe survivorship for the given insurance from time zero to time.\n\n\n\n\n\n","category":"method"},{"location":"api/#Unexported-API","page":"API Reference","title":"Unexported API","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Modules = [LifeContingencies]\nPublic = false","category":"page"},{"location":"api/#LifeContingencies.Contingency","page":"API Reference","title":"LifeContingencies.Contingency","text":"Contingency()\n\nAn abstract type representing the different triggers for contingent benefits. Available options to use include:\n\nLastSurvivor()\n\n\n\n\n\n","category":"type"},{"location":"api/#LifeContingencies.JointAssumption","page":"API Reference","title":"LifeContingencies.JointAssumption","text":"JointAssumption()\n\nAn abstract type representing the different assumed relationship between the survival of the lives on a JointLife. Available options to use include:\n\nFrasier()\n\n\n\n\n\n","category":"type"},{"location":"api/#LifeContingencies.C-Tuple{LifeContingency, Any}","page":"API Reference","title":"LifeContingencies.C","text":"C(lc::LifeContingency, to_time)\n\nC_x is a retrospective actuarial commutation function which is the product of the discount factor and the difference in l (l_x).\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.D-Tuple{LifeContingency, Any}","page":"API Reference","title":"LifeContingencies.D","text":"D(lc::LifeContingency, to_time)\n\nD_x is a retrospective actuarial commutation function which is the product of the survival and discount factor.\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.M-Tuple{LifeContingency, Any}","page":"API Reference","title":"LifeContingencies.M","text":"M(lc::LifeContingency, from_time)\n\nThe M_x actuarial commutation function where the from_time argument is x. Issue age is based on the issue_age in the LifeContingency lc.\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.N-Tuple{LifeContingency, Any}","page":"API Reference","title":"LifeContingencies.N","text":"N(lc::LifeContingency, from_time)\n\nN_x is a prospective actuarial commutation function which is the sum of the D (D_x) values from the given time to the end of the mortality table.\n\n\n\n\n\n","category":"method"},{"location":"api/#LifeContingencies.l-Tuple{LifeContingency, Any}","page":"API Reference","title":"LifeContingencies.l","text":"l(lc::LifeContingency, to_time)\n\nl_x is a retrospective actuarial commutation function which is the survival up to a certain point in time. By default, will have a unitary basis (ie 1.0), but you can specify basis keyword argument to use something different (e.g. 1000 is common in the literature.)\n\n\n\n\n\n","category":"method"},{"location":"api/#MortalityTables.decrement-Tuple{LifeContingency, Any, Any}","page":"API Reference","title":"MortalityTables.decrement","text":"decrement(lc::LifeContingency,to_time)\ndecrement(lc::LifeContingency,from_time,to_time)\n\nReturn the probability of death for the given LifeContingency, with decrements beginning at time zero. \n\nExamples\n\njulia> q = [.1,.2,.3,.4];\n\njulia> l = SingleLife(mortality=q);\n\njulia> survival(l,1)\n0.9\n\njulia> decrement(l,1)\n0.09999999999999998\n\njulia> survival(l,1,2)\n0.8\n\njulia> decrement(l,1,2)\n0.19999999999999996\n\njulia> survival(l,1,3)\n0.5599999999999999\n\njulia> decrement(l,1,3)\n0.44000000000000006\n\n\n\n\n\n","category":"method"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Please open an issue if you encounter any issues or confusion with the package.","category":"page"},{"location":"#LifeContingencies.jl","page":"Home","title":"LifeContingencies.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"(Image: Stable) (Image: Dev) (Image: ) (Image: codecov)","category":"page"},{"location":"","page":"Home","title":"Home","text":"LifeContingencies is a package enabling actuarial life contingent calculations.","category":"page"},{"location":"#Features","page":"Home","title":"Features","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Integration with other JuliaActuary packages such as MortalityTables.jl\nFast calculations, with some parts utilizing parallel processing power automatically\nUse functions that look more like the math you are used to (e.g. A, ä) with Unicode support\nAll of the power, speed, convenience, tooling, and ecosystem of Julia\nFlexible and modular modeling approach","category":"page"},{"location":"#Package-Overview","page":"Home","title":"Package Overview","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Leverages MortalityTables.jl for","category":"page"},{"location":"","page":"Home","title":"Home","text":"the mortality calculations","category":"page"},{"location":"","page":"Home","title":"Home","text":"Contains common insurance calculations such as:\nInsurance(life,yield): Whole life\nInsurance(life,yield,n): Term life for n years\nä(life,yield): present_value of life-contingent annuity\nä(life,yield,n): present_value of life-contingent annuity due for n years\nContains various commutation functions such as D(x),M(x),C(x), etc.\nSingleLife and JointLife capable\nInterest rate mechanics via Yields.jl\nMore documentation available by clicking the DOCS badges at the top of this README","category":"page"},{"location":"#Examples","page":"Home","title":"Examples","text":"","category":"section"},{"location":"#Basic-Functions","page":"Home","title":"Basic Functions","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Calculate various items for a 30-year-old male nonsmoker using 2015 VBT base table and a 5% interest rate","category":"page"},{"location":"","page":"Home","title":"Home","text":"\nusing LifeContingencies\nusing MortalityTables\nusing Yields\nimport LifeContingencies: V, ä # pull the shortform notation into scope\n\n# load mortality rates from MortalityTables.jl\nvbt2001 = MortalityTables.table(\"2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB\")\n\nissue_age = 30\nlife = SingleLife( # The life underlying the risk\n mort = vbt2001.select[issue_age], # -- Mortality rates\n)\n\nyield = Yields.Constant(0.05) # Using a flat 5% interest rate\n\nlc = LifeContingency(life, yield) # LifeContingency joins the risk with interest\n\n\nins = Insurance(lc) # Whole Life insurance\nins = Insurance(life, yield) # alternate way to construct","category":"page"},{"location":"","page":"Home","title":"Home","text":"With the above life contingent data, we can calculate vectors of relevant information:","category":"page"},{"location":"","page":"Home","title":"Home","text":"cashflows(ins) # A vector of the unit cashflows\ntimepoints(ins) # The timepoints associated with the cashflows\nsurvival(ins) # The survival vector\nsurvival(ins,time) # The survivorship through `time`\nbenefit(ins) # The unit benefit vector\nprobability(ins) # The probability of benefit payment\npresent_value(ins) # the present value of the insurance benefits from time zero\npresent_value(ins,time) # the present value of the insurance benefits from `time`","category":"page"},{"location":"","page":"Home","title":"Home","text":"Some of the above will return lazy results. For example, cashflows(ins) will return a Generator which can be efficiently used in most places you'd use a vector of cashflows (e.g. pv(...) or sum(...)) but has the advantage of being non-allocating (less memory used, faster computations). To get a computed vector instead of the generator, simply call collect(...) on the result: collect(cashflows(ins)).","category":"page"},{"location":"","page":"Home","title":"Home","text":"Or calculate summary scalars:","category":"page"},{"location":"","page":"Home","title":"Home","text":"present_value(ins) # The actuarial present value\npremium_net(lc) # Net whole life premium \nV(lc,5) # Net premium reserve for whole life insurance at time 5","category":"page"},{"location":"","page":"Home","title":"Home","text":"Other types of life contingent benefits:","category":"page"},{"location":"","page":"Home","title":"Home","text":"Insurance(lc,10) # 10 year term insurance\nAnnuityImmediate(lc) # Whole life annuity due\nAnnuityDue(lc) # Whole life annuity due\nä(lc) # Shortform notation\nä(lc, 5) # 5 year annuity due\nä(lc, 5, certain=5,frequency=4) # 5 year annuity due, with 5 year certain payable 4x per year\n... # and more!","category":"page"},{"location":"#Constructing-Lives","page":"Home","title":"Constructing Lives","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"SingleLife(vbt2001.select[50]) # no keywords, just a mortality vector\nSingleLife(vbt2001.select[50],issue_age = 60) # select at 50, but now 60\nSingleLife(vbt2001.select,issue_age = 50) # use issue_age to pick the right select vector\nSingleLife(mortality=vbt2001.select,issue_age = 50) # mort can also be a keyword\n","category":"page"},{"location":"#Net-Premium-for-Term-Policy-with-Stochastic-rates","page":"Home","title":"Net Premium for Term Policy with Stochastic rates","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Use a stochastic interest rate calculation to price a term policy:","category":"page"},{"location":"","page":"Home","title":"Home","text":"using LifeContingencies, MortalityTables\nusing Distributions\n\nvbt2001 = MortalityTables.table(\"2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB\")\n\n# use an interest rate that's normally distirbuted\nμ = 0.05\nσ = 0.01\n\nyears = 100\nint = Yields.Forward(rand(Normal(μ,σ), years))\n\nlife = SingleLife(mortality = vbt2001.select[30], issue_age = 30)\n\nterm = 10\nLifeContingencies.A(lc, term) # around 0.055","category":"page"},{"location":"#Extending-example-to-use-autocorrelated-interest-rates","page":"Home","title":"Extending example to use autocorrelated interest rates","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"You can use autocorrelated interest rates - substitute the following in the prior example using the ability to self reference:","category":"page"},{"location":"","page":"Home","title":"Home","text":"σ = 0.01\ninitial_rate = 0.05\nvec = fill(initial_rate, years)\n\nfor i in 2:length(vec)\n vec[i] = rand(Normal(vec[i-1], σ))\nend\n\nint = Yields.Forward(vec)","category":"page"},{"location":"#Premium-comparison-across-Mortality-Tables","page":"Home","title":"Premium comparison across Mortality Tables","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Compare the cost of annual premium, whole life insurance between multiple tables visually:","category":"page"},{"location":"","page":"Home","title":"Home","text":"using LifeContingencies, MortalityTables, Plots\n\ntables = [\n MortalityTables.table(\"1980 CET - Male Nonsmoker, ANB\"),\n MortalityTables.table(\"2001 VBT Residual Standard Select and Ultimate - Male Nonsmoker, ANB\"),\n MortalityTables.table(\"2015 VBT Male Non-Smoker RR100 ANB\"),\n ]\n\nissue_ages = 30:90\nint = Yields.Constant(0.05)\n\nwhole_life_costs = map(tables) do t\n map(issue_ages) do ia\n lc = LifeContingency(SingleLife(mortality = t.ultimate, issue_age = ia), int)\n premium_net(lc)\n\n end\nend\n\nplt = plot(ylabel=\"Annual Premium per unit\", xlabel=\"Issue Age\",\n legend=:topleft, legendfontsize=8,size=(800,600))\n\nfor (i,t) in enumerate(tables)\n plot!(plt,issue_ages,whole_life_costs[i], label=\"$(t.metadata.name)\")\nend\n\ndisplay(plt)","category":"page"},{"location":"","page":"Home","title":"Home","text":"(Image: Comparison of three different mortality tables' effect on insurance cost)","category":"page"},{"location":"#Joint-Life","page":"Home","title":"Joint Life","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"m1 = MortalityTables.table(\"1986-92 CIA – Male Smoker, ANB\")\nm2 = MortalityTables.table(\"1986-92 CIA – Female Nonsmoker, ANB\")\nl1 = SingleLife(mortality = m1.ultimate, issue_age = 40)\nl2 = SingleLife(mortality = m2.ultimate, issue_age = 37)\n\njl = JointLife(lives=(l1, l2), contingency=LastSurvivor(), joint_assumption=Frasier())\n\n\nInsurance(jl,Yields.Constant(0.05)) # whole life insurance\n... # similar functions as shown in the first example above","category":"page"},{"location":"#Commutation-and-Unexported-Function-shorthand","page":"Home","title":"Commutation and Unexported Function shorthand","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Because it's so common to use certain variables in your own code, LifeContingencies avoids exporting certain variables/functions so that it doesn't collide with your own usage. For example, you may find yourself doing something like:","category":"page"},{"location":"","page":"Home","title":"Home","text":"a = ...\nb = ...\nresult = b - a","category":"page"},{"location":"","page":"Home","title":"Home","text":"If you imported using LifeContingencies and the package exported a (annuity_immediate) then you could have problems if you tried to do the above. To avoid this, we only export long-form functions like annuity_immediate. To utilize the shorthand, you can include them into your code's scope like so:","category":"page"},{"location":"","page":"Home","title":"Home","text":"using LifeContingencies # brings all the default functions into your scope\nusing LifeContingencies: a, ä # also brings the short-form annuity functions into scope","category":"page"},{"location":"","page":"Home","title":"Home","text":"Or you can do the following:","category":"page"},{"location":"","page":"Home","title":"Home","text":"using LifeContingencies # brings all the default functions into your scope\n... # later on in the code\nLifeContingencies.ä(...) # utilize the unexported function with the module name","category":"page"},{"location":"","page":"Home","title":"Home","text":"For more on module scoping, see the Julia Manual section.","category":"page"},{"location":"#Actuarial-notation-shorthand","page":"Home","title":"Actuarial notation shorthand","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"V => reserve_premium_net\nv => discount\nA => present value of Insurance\nä => present value of AnnuityDue\na => present value of AnnuityImmediate\nP => premium_net\nω => omega","category":"page"},{"location":"#Commutation-functions","page":"Home","title":"Commutation functions","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"l,\nD,\nM,\nN,\nC,","category":"page"},{"location":"#References","page":"Home","title":"References","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Life Insurance Mathematics, Gerber\nActuarial Mathematics and Life-Table Statistics, Slud\nCommutation Functions, MacDonald","category":"page"},{"location":"","page":"Home","title":"Home","text":"\n","category":"page"}] +} diff --git a/v2.5.0/siteinfo.js b/v2.5.0/siteinfo.js new file mode 100644 index 0000000..19b29ce --- /dev/null +++ b/v2.5.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v2.5.0"; diff --git a/versions.js b/versions.js index 705f916..9928613 100644 --- a/versions.js +++ b/versions.js @@ -1,5 +1,6 @@ var DOC_VERSIONS = [ "stable", + "v2.5", "v2.4", "v2.3", "v2.2", @@ -15,5 +16,5 @@ var DOC_VERSIONS = [ "v0.6", "dev", ]; -var DOCUMENTER_NEWEST = "v2.4.0"; +var DOCUMENTER_NEWEST = "v2.5.0"; var DOCUMENTER_STABLE = "stable";