README- ::logarithmicChart::logarithmic
- ::newChart::new
- ::renderChart::render
- ::seriesChart::series
- ::sizeChart::size
- ::subtitleChart::subtitle
- ::x_labelChart::x_label
- ::y_labelChart::y_label
- ::chinese_nameChinaTable::chinese_name
- ::codeChinaTable::code
- ::english_nameChinaTable::english_name
- ::is_pensionChinaTable::is_pension
- ::of_codeChinaTable::of_code
- ::qxChinaTable::qx
- ::tableChinaTable::table
- TCommutation
- ::parseFractionalAge::parse
- ::accumulateInterest::accumulate
- ::accumulated_dueInterest::accumulated_due
- ::accumulated_immediateInterest::accumulated_immediate
- ::accumulation_factorInterest::accumulation_factor
- ::annualInterest::annual
- ::annuity_continuousInterest::annuity_continuous
- ::annuity_dueInterest::annuity_due
- ::annuity_due_mthlyInterest::annuity_due_mthly
- ::annuity_immediateInterest::annuity_immediate
- ::annuity_immediate_mthlyInterest::annuity_immediate_mthly
- ::decreasing_annuityInterest::decreasing_annuity
- ::discountInterest::discount
- ::discount_factorInterest::discount_factor
- ::discount_rateInterest::discount_rate
- ::forceInterest::force
- ::increasing_annuityInterest::increasing_annuity
- ::nominalInterest::nominal
- ::nominal_discountInterest::nominal_discount
- ::ofInterest::of
- ::of_discount_rateInterest::of_discount_rate
- ::of_forceInterest::of_force
- ::of_nominalInterest::of_nominal
- ::perpetuityInterest::perpetuity
- ::perpetuity_dueInterest::perpetuity_due
- ::curtate_expectationLifeTable::curtate_expectation
- ::death_probabilityLifeTable::death_probability
- ::deferred_death_probabilityLifeTable::deferred_death_probability
- ::dxLifeTable::dx
- ::expectationLifeTable::expectation
- ::fractionLifeTable::fraction
- ::from_qxLifeTable::from_qx
- ::idLifeTable::id
- ::labelLifeTable::label
- ::limiting_ageLifeTable::limiting_age
- ::lxLifeTable::lx
- ::person_yearsLifeTable::person_years
- ::pxLifeTable::px
- ::qxLifeTable::qx
- ::radixLifeTable::radix
- ::survivalLifeTable::survival
- ::total_person_yearsLifeTable::total_person_years
- ::ofPoint::of
- TSeries
- ::annual_premium_endowmentValuation::annual_premium_endowment
- ::annual_premium_limitedValuation::annual_premium_limited
- ::annual_premium_termValuation::annual_premium_term
- ::annual_premium_whole_lifeValuation::annual_premium_whole_life
- ::commutation_cValuation::commutation_c
- ::commutation_dValuation::commutation_d
- ::commutation_mValuation::commutation_m
- ::commutation_nValuation::commutation_n
- ::commutation_rValuation::commutation_r
- ::commutation_sValuation::commutation_s
- ::continuous_annuityValuation::continuous_annuity
- ::continuous_insuranceValuation::continuous_insurance
- ::decreasing_term_insuranceValuation::decreasing_term_insurance
- ::deferred_annuityValuation::deferred_annuity
- ::deferred_insuranceValuation::deferred_insurance
- ::endowment_insuranceValuation::endowment_insurance
- ::increasing_annuityValuation::increasing_annuity
- ::increasing_insuranceValuation::increasing_insurance
- ::increasing_term_insuranceValuation::increasing_term_insurance
- ::insurance_annuity_identityValuation::insurance_annuity_identity
- ::interestValuation::interest
- ::life_tableValuation::life_table
- ::limiting_ageValuation::limiting_age
- ::ofValuation::of
- ::pure_endowmentValuation::pure_endowment
- ::reserve_endowmentValuation::reserve_endowment
- ::reserve_retrospectiveValuation::reserve_retrospective
- ::reserve_schedule_facklerValuation::reserve_schedule_fackler
- ::reserve_stepValuation::reserve_step
- ::reserve_termValuation::reserve_term
- ::reserve_whole_lifeValuation::reserve_whole_life
- ::temporary_annuityValuation::temporary_annuity
- ::term_insuranceValuation::term_insurance
- ::whole_life_annuityValuation::whole_life_annuity
- ::whole_life_annuity_immediateValuation::whole_life_annuity_immediate
- ::whole_life_insuranceValuation::whole_life_insurance
- Vall_china_tables
- Vcl1_qx
- Vcl2_qx
- Vcl3_qx
- Vcl4_qx
- Vcl5_qx
- Vcl6_qx
- Vfixed
- Vpad_left
- Vpad_right
- Vpercent
- Vrule
moonactuary
Actuarial library for the China Life Insurance Mortality Table (CL 2010-2013): survivorship, commutation columns, net single and annual premiums, and reserves by three independent methods, with a command line tool and a dependency-free SVG chart renderer.
actuarial
actuarial-science
life-insurance
life-table
mortality
china
cl2010-2013
reserves
Author
Version
0.1.1
License
Apache-2.0
Repository
Last updated
2 hours ago
Downloads
4
#moonactuary
用 MoonBit 实现的中国人身保险业经验生命表（CL 2010-2013）寿险精算库，以及一个可以把它全部功能跑一遍的命令行工具。
- 六张经验表（CL1–CL6）的生存函数、换算函数、纯保费与准备金
- 趸缴纯保费、年缴均衡纯保费，终身 / 定期 / 两全三种形态
- 准备金三条独立路径：前瞻法、后顾法、Fackler 递推，互为交叉校核
- 零第三方依赖（仅用 MoonBit 标准库），可在 wasm、wasm-gc、js、native 四个后端构建
- 内置 SVG 绘图，对数刻度，用于读死亡率与生存曲线
#项目目标
中国人身保险业经验生命表（2010-2013）是中国寿险产品定价与法定准备金评估的基准表，但公开可复用的实现并不多，尤其缺少能自我校核的实现。这个项目的目标是：
- 把六张表做成可复用的库，生存函数严格复现行内公布的 Lx、Tx、ex；
- 让结论可以自证：第一原则恒等式 1 = A_x + d·ä_x 在 6 张表 × 3 利率 × 7 年龄上残差为 0，准备金三条路径互相印证，第 n 年末准备金恰等于满期给付额；
- 一条命令复现全部核心路径，任何人拿到仓库都能用 moon run cmd/main demo 看到同样一组数字；
- 保持零依赖与多后端，使它可以嵌入 WASM 前端、评估脚本或服务端程序。
#环境要求
| 项 | 要求 | 本项目验证环境 |
|---|---|---|
| MoonBit 编译器 | moonc ≥ 0.10.14 | v0.10.19+97801ee1b |
| 构建工具 | moon 工具链 | moon 0.1.20261029 |
| 第三方依赖 | 无 | — |
#安装
#作为库使用
moon add hua1104/moonactuary#从源码构建命令行工具
# 安装 MoonBit 工具链（Linux / macOS）
curl -fsSL https://cli.moonbitlang.com/install/unix.sh | bash
export PATH="$HOME/.moon/bin:$PATH"
git clone https://github.com/hua1104/moonactuary.git
cd moonactuary
moon build --target native # 产物：_build/native/debug/build/cmd/main/main.exe
moon build --target all # 同时产出 wasm / wasm-gc / js / native不构建也可以直接运行，moon run 会自行编译：
moon run cmd/main demo#快速开始（库）
仓库里有一个可运行的最小样例，打印的就是下面这段代码的结果：
$ moon run examples/quickstart
CL1 非养老类业务一表（男）
30 岁生存人数 l30 986359
30 岁平均余命 e30 47.25
两全保险趸缴纯保费 A 0.614601
年缴均衡纯保费 P 0.038895
第 10 年末准备金 V 0.437487对应代码（examples/quickstart/main.mbt）：
// 取一张经验表，构造（表, 利率）估值对
let china = @moonactuary.ChinaTable::of_code("CL1").unwrap()
let table = china.table()
let v = @moonactuary.Valuation::of(
table=table,
interest=@moonactuary.Interest::of(0.025), // 预定利率 2.5%
)
// 生存函数
println(table.lx(30)) // 986359
println(table.expectation(30)) // 47.25，30 岁男性的平均余命
// 两全保险趸缴纯保费与年缴均衡纯保费
println(v.endowment_insurance(30, 20)) // 0.614601
println(v.annual_premium_endowment(30, 20)) // 0.038895
// 准备金：前瞻法
let premium = v.annual_premium_endowment(30, 20)
println(v.reserve_endowment(30, 20, 10, premium)) // 0.437487，第 10 年末#命令行
moonactuary <命令> [选项]| 命令 | 作用 |
|---|---|
| tables | 列出六张经验表及其零岁平均余命 |
| table | 打印生命表函数 lx / dx / Lx / Tx / ex |
| premium | 计算趸缴纯保费与年缴均衡纯保费 |
| compare | 按相同产品假设对比六张经验表的保费结果 |
| reserve | 打印逐年准备金表（前瞻 / 后顾 / Fackler 三列） |
| plot | 生成 SVG 曲线，输出到标准输出 |
| demo | 最小演示：一条命令触发全部核心功能路径 |
| verify | 一键验收：跨六张表、三档利率、三类产品交叉校核 |
| 选项 | 含义 | 默认 |
|---|---|---|
| --table | 经验表 CL1–CL6 | CL1 |
| --age | 投保年龄 | 30 |
| --term | 保险期间（年） | 20 |
| --rate | 预定利率百分数，如 2.5 表示 2.5% | 2.5 |
| --product | 险种 whole（终身）/ term（定期）/ endowment（两全） | endowment |
| --from --to | 生命表年龄区间 | 0 105 |
| --kind | 曲线 mortality / survival | mortality |
| --format | compare 输出格式 table / csv | table |
| --help | 打印用法 | — |
#示例
$ moon run cmd/main tables
中国人身保险业经验生命表（2010-2013）
代码 业务表 e0 e20 e40 e60
------------------------------------------------------------
CL1 非养老类业务一表（男） 76.42 56.93 37.71 20.03
CL2 非养老类业务一表（女） 81.71 62.05 42.43 23.62
CL3 非养老类业务二表（男） 80.35 60.74 41.38 23.21
CL4 非养老类业务二表（女） 85.44 65.68 45.98 26.94
CL5 养老类业务表（男） 83.13 63.44 43.90 25.34
CL6 养老类业务表（女） 88.13 68.33 48.55 29.30$ moon run cmd/main premium --product whole --age 40 --rate 3.0
CL1 · 终身寿险 · 投保年龄 40 · 期间 20 年 · 利率 3.00%
----------------------------------------------------
趸缴纯保费 0.343820
年缴均衡纯保费 0.015261六张表横向比较，并导出 CSV：
moon run cmd/main compare --product term --age 40 --term 10 --rate 3.5
moon run cmd/main compare --format csv > premiums.csv$ moon run cmd/main table --from 30 --to 32
CL1 非养老类业务一表（男） · 生命表函数（基数 1,000,000）
------------------------------------------------------------------------------------
年龄 qx lx dx Lx Tx ex
------------------------------------------------------------------------------------
30 0.000797 986359 786 985966 46602129 47.25
31 0.000847 985573 835 985156 45616162 46.28
32 0.000903 984738 889 984294 44631007 45.32$ moon run cmd/main reserve --term 5
CL1 · 两全保险 · 投保年龄 30 · 期间 5 年 · 年缴保费 0.185955
------------------------------------------------------------------
年度 年龄 前瞻准备金 后顾准备金 Fackler 偏差
------------------------------------------------------------------
0 30 0.000000 0.000000 0.000000 0.00
1 31 0.189958 0.189958 0.189958 0.00
2 32 0.384790 0.384790 0.384790 0.00
3 33 0.584638 0.584638 0.584638 0.00
4 34 0.789655 0.789655 0.789655 0.00
5 35 1.000000 1.000000 1.000000 0.00$ moon run cmd/main plot --kind mortality > qx.svg # 对数刻度死亡率曲线
$ moon run cmd/main plot --kind survival > lx.svg # 生存人数曲线#最小演示（可复现）
demo 一条命令走完教科书校核、恒等式扫描、保费计算与准备金三条路径：
$ moon run cmd/main demo
moonactuary demo — CL(2010-2013) 寿险精算最小演示
中国人身保险业经验生命表（2010-2013）
代码 业务表 e0 e20 e40 e60
------------------------------------------------------------
CL1 非养老类业务一表（男） 76.42 56.93 37.71 20.03
CL2 非养老类业务一表（女） 81.71 62.05 42.43 23.62
CL3 非养老类业务二表（男） 80.35 60.74 41.38 23.21
CL4 非养老类业务二表（女） 85.44 65.68 45.98 26.94
CL5 养老类业务表（男） 83.13 63.44 43.90 25.34
CL6 养老类业务表（女） 88.13 68.33 48.55 29.30
【教科书基准校核】CL1 生存函数
参照：l0/d0/L0/T0/e0 = 1000000 / 867 / 999567 / 76420142 / 76.42
年龄 qx lx dx Lx Tx ex
0 0.000867 1000000 867 999567 76420142 76.42
1 0.000615 999133 614 998826 75420575 75.49
2 0.000445 998519 444 998296 74421750 74.53
3 0.000339 998074 338 997905 73423453 73.57
4 0.000280 997736 279 997596 72425548 72.59
5 0.000251 997456 250 997331 71427952 71.61
101 0.476447 1658 790 1263 2409 1.45
105 1.000000 85 85 43 43 0.50
【第一原则恒等式】1 = A_x + d · ä_x
6 张表 × 3 利率 × 7 年龄，残差上限 0.00
【示例保单】CL1 · 两全保险 · 投保年龄 30 · 期间 20 年 · 预定利率 2.50%
趸缴纯保费 0.614601
年缴均衡纯保费 0.038895
【准备金三条路径】前瞻法 / 后顾法 / Fackler 递推
年度 年龄 前瞻法 后顾法 Fackler 偏差
------------------------------------------------------------------
0 30 0.000000 0.000000 0.000000 0.00
1 31 0.039102 0.039102 0.039102 0.00
...
19 49 0.936714 0.936714 0.936714 0.00
20 50 1.000000 1.000000 1.000000 0.00
三条独立路径最大偏差 0.00，第 20 年末准备金为 1.000000（等于满期给付额）上文中 ... 处为第 2–18 保单年度，数值逐年递增，命令本身会打印完整的 21 行。
#一键验收
评审或维护者可以运行 moon run cmd/main verify，自动对六张经验表、三档利率与三类产品执行恒等式及准备金交叉校核。成功时输出：
moonactuary acceptance verification
生命表：6 张 CL(2010-2013) 经验表
利率：2.5% / 3.0% / 3.5%
产品：终身寿险 / 定期寿险 / 两全保险
恒等式校核：126 项，最大残差 0.000000000000
准备金校核：1134 项，最大偏差 0.000000000000
PASS：全部核心精算路径交叉校核通过CLI 会在计算前检查经验表代码、产品名称、年龄、期间、利率和绘图类型。非法输入会显示明确错误，不会静默替换为默认值或触发数组越界。
#数据来源与校核
qx 取自中国精算师协会发布的《中国人身保险业经验生命表（2010-2013）》，六张表分别为非养老类业务一表、二表（男、女）与养老类业务表（男、女）。生存函数在基数 1,000,000 与均匀死亡分布（UDD）假设下递推，Lx、Tx、ex 与教材中公布的 CL1 数值逐行一致（l0/d0/L0/T0/e0 = 1000000 / 867 / 999567 / 76420142 / 76.42）。除 UDD 外，库内还支持死亡力恒定（CFM）与 Balducci 双曲线两种分数年龄假设。
#项目结构
.
├── cltables.mbt 六张经验表的 qx 数据与业务分类
├── lifetable.mbt 生存函数递推、分数年龄假设、概率函数
├── interest.mbt 利息理论：名义/贴现/力、各类年金
├── valuation.mbt 换算列 D C M N R S 与生命年金
├── insurance.mbt 趸缴/年缴纯保费、准备金、变额保险
├── tables.mbt ChinaTable 枚举与元数据
├── fmt.mbt 定点小数与对齐排版
├── svg.mbt 零依赖 SVG 渲染器（支持对数轴）
├── *_test.mbt 黑盒与白盒测试
├── examples/
│ └── quickstart/ 最小可运行样例
├── cli/ 命令行前端：参数解析与六个子命令
│ ├── args.mbt
│ ├── commands.mbt
│ └── run.mbt
└── cmd/main/ 可执行文件入口（把 argv 交给 cli，仅此而已）#测试
moon test # 62 项测试
moon coverage analyze # 覆盖率报告测试分三层：教科书公布值的逐行校核、与定义式求和的交叉验证（公式与其实现必须错成完全一样才能蒙混过关）、以及边界与退化输入（零利率、空期间、超范围年龄、单点与常量序列）。
#本地一键验收
Linux / macOS：
bash scripts/acceptance.shWindows PowerShell：
powershell -ExecutionPolicy Bypass -File scripts/acceptance.ps1Windows 脚本默认验证 wasm、wasm-gc 和 JavaScript 后端；安装 MSVC Build Tools 后也可以直接运行 moon build --target native。
#持续集成
.github/workflows/ci.yml 在每次推送与每个 PR 上执行：
| 阶段 | 命令 |
|---|---|
| 检查 | moon check --target all |
| 构建 | moon build --target all（wasm / wasm-gc / js / native） |
| 测试 | moon test --target all |
| 格式 | moon fmt --check |
| 接口 | moon info 后确认 .mbti 无漂移 |
| 冒烟 | 运行 demo / tables / premium / reserve 并核对关键数字 |
黑客松评审的快速复现步骤、项目亮点和两分钟演示路线见 HACKATHON.md。
正式项目申报内容见 APPLICATION.md。
#许可证
Apache License 2.0。六张经验表的 qx 数据为行业公开发布的标准数据；实现为本项目原创。
Chart
A chart: one or more series sharing axes.
Chart::logarithmic
Draw the vertical axis on a logarithmic scale.
Chart::new
A chart with sensible defaults, all of which can be overridden by rebuilding
the value with the builders below.
Chart::render
Render the chart to a standalone SVG document.
Chart::series
Append a series to the chart.
Chart::size
Override the output pixel size.
Chart::subtitle
Set the chart subtitle.
Chart::x_label
Label the horizontal axis.
ChinaTable
pub enum ChinaTable {
NonPensionIMale
NonPensionIFemale
NonPensionIIMale
NonPensionIIFemale
PensionMale
PensionFemale
}One of the six tables published as the China Life Insurance Mortality Table
(2010-2013). The three business lines differ substantially in observed
longevity and are mandated for different product types: pension business
carries the longest expected lifetimes and so the highest reserves.
ChinaTable::chinese_name
The Chinese name of the table.
ChinaTable::code
The short code used by the regulator, for example "CL1".
ChinaTable::english_name
The English name of the table.
ChinaTable::is_pension
Whether the table is intended for pension (养老) business, which exhibits
the longest observed lifetimes of the three business lines.
ChinaTable::of_code
Look a table up by its regulator code, accepting "CL1" through "CL6" in
either case. all_china_tables remains the way to enumerate them.
ChinaTable::qx
The raw annual mortality rates qx for ages 0 through 105.
ChinaTable::table
Build a full LifeTable from this table. The default radix of 1,000,000
reproduces the survivorship columns published alongside CL(2010-2013).
Commutation
The six classical commutation columns over ages 0 through omega.
FractionalAge
pub enum FractionalAge {
UniformDeaths
ConstantForce
Hyperbolic
}An assumption used to interpolate the survivorship function between two
consecutive integer ages. The published CL(2010-2013) values of Lx are
reproduced exactly by UniformDeaths.
FractionalAge::parse
Parse a fractional age assumption by name, accepting the common
abbreviations "udd", "cfm" and "balducci" plus their full English names.
Used by the command line front end and by callers loading a table from
configuration.
Interest
pub struct Interest {
rate : Double
}A compound interest environment described by its effective annual rate i.
Every other quantity used in actuarial mathematics derives from i: the
discount factor v, the effective annual discount rate d, the force of
interest delta, and nominal rates convertible m times per year. Modelling
these conversions explicitly is what keeps reserve recursion and premium
algebra consistent with each other.
Interest::accumulate
Accumulation a(t) = (1 + i)^t from time 0 to time t. Accepts fractional
years, and extrapolates backwards for negative t.
Interest::accumulated_due
s-double-dot_n: accumulated value at time n of payments of 1 at the start
of each of n years.
Interest::accumulated_immediate
s_n: accumulated value at time n of payments of 1 at the end of each of
n years.
Interest::accumulation_factor
The annual accumulation factor 1 + i.
Interest::annual
The effective annual interest rate i.
Interest::annuity_continuous
a-bar_n: present value of an annuity payable continuously at rate 1 per
year for n years.
Interest::annuity_due
a-double-dot_n: present value of an annuity-due paying 1 at the start of
each of n years, first payment immediate.
Interest::annuity_due_mthly
a-double-dot_n^(m): present value of an annuity paying 1/m at the start of
each m-th of a year for n years. This is the shape of a monthly premium
annuity, and is what Chinese monthly-pay products are valued from.
Interest::annuity_immediate
a_n: present value of an annuity-immediate paying 1 at the end of each of
n years. Payments stop at year n.
Interest::annuity_immediate_mthly
a_n^(m): present value of an annuity paying 1/m at the end of each m-th of
a year for n years.
Interest::decreasing_annuity
(Da)_n: present value of a decreasing annuity-immediate paying n at the end
of year 1, n-1 at the end of year 2, down to 1 at the end of year n.
Interest::discount
Discount v^t = (1 + i)^(-t): the value at time 0 of one unit payable at
time t.
Interest::discount_factor
The annual discount factor v = 1 / (1 + i).
Interest::discount_rate
The effective annual discount rate d = i / (1 + i) = i * v.
Interest::force
The constant force of interest delta = ln(1 + i) equivalent to i.
Interest::increasing_annuity
(Ia)_n: present value of an increasing annuity-immediate paying 1 at the
end of year 1, 2 at the end of year 2, up to n at the end of year n.
Interest::nominal
The nominal rate i^(m) convertible m times per year. Twelve is the
monthly conversion used by Chinese products that collect premiums monthly.
Interest::nominal_discount
The nominal discount rate d^(m) convertible m times per year.
Interest::of
An interest environment at effective annual rate rate. A rate of 0.025
means 2.5% (预定利率); negative rates are rejected as they have no
actuarial reading and make accumulation ill-behaved.
Interest::of_discount_rate
Given a discount rate d convertible once per year, recover the effective
annual interest rate i = d / (1 - d).
Interest::of_force
Given a constant force of interest delta, recover the effective annual
rate i = e^delta - 1.
Interest::of_nominal
Given a nominal rate i^(m) convertible m times per year, recover the
effective annual rate. Inverse of nominal.
Interest::perpetuity
a_infinity: present value of a perpetuity-immediate paying 1 at the end of
every year forever. Only finite when i > 0.
LifeTable
A complete life table. Indices run from 0 to limiting_age() inclusive.
The radix follows the Chinese convention of 1,000,000 lives, matching the
published CL(2010-2013) survivorship columns.
LifeTable::curtate_expectation
The curtate expectation of life（取整余命）at age x: the expected number
of whole future years survived, excluding the final partial year. Under the
uniform distribution of deaths this sits exactly half a year below the
complete expectation.
LifeTable::death_probability
t q x: the probability that a life aged x dies within the next t years.
LifeTable::deferred_death_probability
t | q x: the probability that a life aged x survives t years and then
dies during the following year.
LifeTable::dx
Deaths dx occurring between ages x and x + 1.
LifeTable::expectation
The complete expectation of life ex（平均余命）at exact age x, counting
fractional years.
LifeTable::fraction
The fractional age assumption the table was built under.
LifeTable::from_qx
fn LifeTable::from_qx(qx~ : Array[Double], id? : String, label? : String, radix? : Double, fraction? : FractionalAge) -> LifeTableBuild a life table from annual death probabilities qx, covering ages 0
through qx.length() - 1 inclusive. The final rate must terminate the
table: survivors reaching the limiting age all die within that year, so
qx[omega] is expected to be 1.0.
LifeTable::id
The identifier of the table source, for example "CL1".
LifeTable::label
A human readable name for the table.
LifeTable::limiting_age
The limiting age omega: every life attaining it dies within that year.
LifeTable::lx
Survivors lx attaining exact age x.
LifeTable::person_years
Person-years Lx lived jointly by survivors of age x over the next year.
LifeTable::px
The annual survival probability px = 1 - qx.
LifeTable::qx
The annual death probability qx at exact integral age x. Ages past omega
report certainty of death; negative ages report zero mortality.
LifeTable::radix
The radix l[0] the table was built from.
LifeTable::survival
t p x: the probability that a life aged x survives at least t more
whole years.
Point
pub struct Point {
x : Double
y : Double
}Series
A labelled run of observations drawn as one polyline.
Valuation
A mortality table paired with an interest assumption. Every actuarial
function in this library is a method on Valuation, so premiums and
reserves computed together always agree on discounting and mortality.
P_{x:n}: net annual premium for n-year endowment insurance, payable for the
full term.
m P_x: net annual premium for whole life insurance payable for at most m
years, after which the policy is paid up. This limited-payment structure is
common in Chinese whole life products.
P_{x:n}^1: net annual premium for n-year term insurance, payable for the
full term.
P_x: net annual premium for whole life insurance, level for life, obtained
by the equivalence principle A_x = P * a-double-dot_x.
Valuation::commutation_c
C_x = v^(x+1) d_x.
Valuation::commutation_d
D_x = v^x l_x.
Valuation::commutation_m
M_x = sum of C_k over k >= x.
Valuation::commutation_n
N_x = sum of D_k over k >= x.
Valuation::commutation_r
R_x = sum of M_k over k >= x.
Valuation::commutation_s
S_x = sum of N_k over k >= x.
Valuation::continuous_annuity
a-bar_x: a continuous whole life annuity paying at rate 1 per year for as
long as (x) survives. Derived from the continuous insurance Ā_x under the
UDD assumption using the identity 1 = Ā_x + delta * a-bar_x, with
Ā_x = (i / delta) * A_x. Falls back to the discrete annuity when the force
of interest degenerates to zero.
Valuation::continuous_insurance
A-double-dot_x^(m): whole life insurance paying at the moment of death,
converted from the end-of-year benefit under UDD by the factor i / delta.
Valuation::decreasing_term_insurance
(DA){x:n}^1: decreasing n-year term insurance paying n - k at the end of
the year of death, where death falls in the (k+1)-th policy year, so the
face amount steps down yearly from n to 1. It relates to the increasing
policy by (n + 1) A{x:n}^1 - (IA)_{x:n}^1.
Valuation::deferred_annuity
u|a-double-dot_x: an annuity-due deferred u years, first payment at age
x + u. Equals N_{x+u} / D_x.
Valuation::deferred_insurance
u|A_x: net single premium for whole life insurance deferred u years, paying
nothing on death during the deferral period.
Valuation::endowment_insurance
A_{x:n}: net single premium for an n-year endowment insurance, which pays 1
either on death within n years or on survival to age x + n. It decomposes
into the term insurance plus the pure endowment.
Valuation::increasing_annuity
(Ia-double-dot)_x: increasing whole life annuity-due paying 1 in the first
year, 2 in the second, and so on. Equals S_x / D_x.
Valuation::increasing_insurance
(IA)_x: increasing whole life insurance paying k + 1 at the end of the year
of death, where k is the number of complete years survived. Equals
R_x / D_x.
Valuation::increasing_term_insurance
(IA){x:n}^1: increasing n-year term insurance paying k + 1 at the end of
the year of death, where death falls in the (k+1)-th policy year. Equals
(R_x - R{x+n} - n * M_{x+n}) / D_x.
Valuation::insurance_annuity_identity
Check the universal identity 1 = A_x + d * a-double-dot_x, which must hold
for any valuation regardless of table or interest rate. Returns the residual
rather than a Boolean so a caller can judge its own tolerance.
Valuation::interest
The interest assumption this valuation was built from.
Valuation::life_table
The mortality table this valuation was built from.
Valuation::limiting_age
The limiting age omega; no life survives past it.
Valuation::of
Build the commutation columns for a table and interest pair.
Valuation::pure_endowment
nE_x: net single premium for a pure endowment paying 1 at time n only if
(x) survives to age x + n. Equals D_{x+n} / D_x.
Valuation::reserve_endowment
t V: the net level terminal reserve at duration t of an n-year endowment
policy, with n - t years remaining at that point.
Valuation::reserve_retrospective
t V computed retrospectively: accumulated premiums net of accumulated
claims, per survivor, grown to duration t. Must agree with the prospective
reserve exactly, which makes it a strong cross-check on both directions.
Valuation::reserve_schedule_fackler
Roll a level net premium reserve forward from duration from to duration
to using only the Fackler recursion, starting from opening. Because the
recursion never looks past the coming year, running it to the end of the
contract and comparing against the prospective reserve validates the entire
premium basis: if the premium is wrong, the two will disagree.
Valuation::reserve_step
One step of the Fackler recursion: roll a terminal reserve forward one
policy year. Given the reserve V_t held at duration t, a premium collected
at the start of year t + 1, mortality q_{x+t} and a unit benefit paid at the
end of the year of death,
(V_t + P) (1 + i) = p_{x+t} V_{t+1} + q_{x+t} b
so the recursion recovers V_{t+1} without referring to any future year.
Valuation::reserve_term
t V: the net level terminal reserve at duration t of an n-year term policy.
Valuation::reserve_whole_life
t V: the net level terminal reserve at duration t for a whole life policy
issued at age x charging net annual premium premium. Computed
prospectively as A_{x+t} - P * a-double-dot_{x+t}.
Valuation::temporary_annuity
a-double-dot_{x:n}: an n-year temporary annuity-due, paying at most n times
at the start of each year while (x) survives. Equals (N_x - N_{x+n}) / D_x.
Valuation::term_insurance
A_{x:n}^1: net single premium for n-year term insurance, paying 1 at the end
of the year of death only if death occurs within n years.
Valuation::whole_life_annuity
a-double-dot_x: expected present value of a whole life annuity-due paying 1
at the start of every year while (x) survives. Equals N_x / D_x.
Valuation::whole_life_annuity_immediate
a_x: the whole life annuity-immediate, paying at the end of each completed
year survived. It is always exactly one payment less than the annuity-due.
all_china_tables
All six tables, in publication order.
cl1_qx
CL1(2010-2013) / 非养老类业务一表（男）
Published by the China Insurance Regulatory Commission (保监发〔2016〕107号,
2016-12-21) as part of the China Life Insurance Mortality Table (2010-2013).
Column 1 of the official six-column table; qx at ages 0..105 inclusive,
with q_105 = 1 by construction (omega = 105).
cl2_qx
CL2(2010-2013) / 非养老类业务一表（女）
Published by the China Insurance Regulatory Commission (保监发〔2016〕107号,
2016-12-21) as part of the China Life Insurance Mortality Table (2010-2013).
Column 2 of the official six-column table; qx at ages 0..105 inclusive,
with q_105 = 1 by construction (omega = 105).
cl3_qx
CL3(2010-2013) / 非养老类业务二表（男）
Published by the China Insurance Regulatory Commission (保监发〔2016〕107号,
2016-12-21) as part of the China Life Insurance Mortality Table (2010-2013).
Column 3 of the official six-column table; qx at ages 0..105 inclusive,
with q_105 = 1 by construction (omega = 105).
cl4_qx
CL4(2010-2013) / 非养老类业务二表（女）
Published by the China Insurance Regulatory Commission (保监发〔2016〕107号,
2016-12-21) as part of the China Life Insurance Mortality Table (2010-2013).
Column 4 of the official six-column table; qx at ages 0..105 inclusive,
with q_105 = 1 by construction (omega = 105).
cl5_qx
CL5(2010-2013) / 养老类业务表（男）
Published by the China Insurance Regulatory Commission (保监发〔2016〕107号,
2016-12-21) as part of the China Life Insurance Mortality Table (2010-2013).
Column 5 of the official six-column table; qx at ages 0..105 inclusive,
with q_105 = 1 by construction (omega = 105).
cl6_qx
CL6(2010-2013) / 养老类业务表（女）
Published by the China Insurance Regulatory Commission (保监发〔2016〕107号,
2016-12-21) as part of the China Life Insurance Mortality Table (2010-2013).
Column 6 of the official six-column table; qx at ages 0..105 inclusive,
with q_105 = 1 by construction (omega = 105).
fixed
fn fixed(value : Double, places : Int) -> StringRender value rounded to places decimal places. Negative values keep
their sign even when rounding to zero, which matters for small reserves.
pad_left
fn pad_left(value : String, width : Int) -> StringRight-align value in a field width characters wide, growing past it
rather than truncating when the content is longer.
pad_right
fn pad_right(value : String, width : Int) -> StringLeft-align value in a field width characters wide.
percent
fn percent(value : Double, places : Int) -> StringRender a value as a percentage with places decimal places.
rule
fn rule(width : Int, pattern : Char) -> StringA horizontal rule of width characters of the given pattern. Used for
table rules without depending on Unicode box drawing.
Install
Download zipActuarial library for the China Life Insurance Mortality Table (CL 2010-2013): survivorship, commutation columns, net single and annual premiums, and reserves by three independent methods, with a command line tool and a dependency-free SVG chart renderer.
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