advanced-short-term-actuarial-mathematics

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Chinese

Advanced Short-Term Actuarial Mathematics

高级短期精算数学

When to Use

适用场景

Select and justify severity families (parametric tails, mixtures) and frequency models (Poisson, negative binomial, mixtures)
Build aggregate loss models: compound distributions, normal approximation limits, FFT/simulation concepts
Apply credibility (Bühlmann, Bühlmann-Straub, limited fluctuation) and experience rating math
Structure ratemaking: pure premium, loss ratio, trend, on-level, indicated change logic
Explain short-term reserving at the mathematical level (chain ladder factors, expected loss ratio)
Estimate parameters (MLE), run goodness-of-fit and diagnostics, interpret residuals and tail fit
Compute risk measures (VaR, TVaR) and relate them to capital concepts at a technical level
Connect modeling choices to pricing and reserving workflows; hand execution to
```
actuarial-analyst
```

选择并论证损失程度分布族（参数化尾部、混合分布）和发生频率模型（泊松分布、负二项分布、混合分布）
构建总损失模型：复合分布、正态近似极限、FFT/模拟概念
应用可信度（Bühlmann、Bühlmann-Straub、有限波动）及经验费率相关数学方法
构建费率厘定逻辑：纯保费、损失率、趋势调整、平准化费率、指示性费率变动逻辑
从数学层面解释短期准备金计提（链梯法因子、预期损失率法）
估计参数（MLE）、开展拟合优度检验与诊断分析、解读残差与尾部拟合效果
计算风险度量指标（VaR、TVaR）并从技术层面关联资本概念
将建模选择与定价及准备金计提流程关联；将实操执行环节转交
```
actuarial-analyst
```

When NOT to Use

不适用场景

Life insurance, annuities, long-term care, or life contingencies (mortality, reserves by policy) →
```
life-health-insurance
```
or longevity-focused skills
Triangle workbooks, exhibit production, statutory tie-outs, or model run packs only →
```
actuarial-analyst
```
Appointed actuary opinions, regulatory sign-off, or enterprise capital policy →
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actuary
```
,
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appointed-chief-actuary
```
Enterprise assumption governance, assumption papers, and change control →
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assumption-setting
```
P&C coverage wording, claims handling, underwriting authority, or DOI filing narrative →
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property-casualty-insurance
```
Exam cram or past-exam solutions as the sole deliverable (support professional application; exam study is secondary)
General data science, ML pipelines, or quant research without actuarial loss-model framing →
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data-scientist
```
,
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quantitative-researcher
```
Chart design and dashboard craft only →
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data-visualization
```
Credential pathway and exam strategy only →
```
associate-actuary
```

人寿保险、年金、长期护理或寿险精算（死亡率、保单准备金）→ 适用
```
life-health-insurance
```
或聚焦长寿风险的技能
仅涉及三角表工作底稿、展示材料制作、法定核对或模型运行包的场景 →
```
actuarial-analyst
```
指定精算师意见、监管签字确认或企业资本政策 →
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actuary
```
、
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appointed-chief-actuary
```
企业假设管理、假设文档及变更控制 →
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assumption-setting
```
财产险条款措辞、理赔处理、核保权限或DOI申报说明 →
```
property-casualty-insurance
```
仅提供备考突击材料或过往考试答案（支持专业应用；考试学习为次要用途）
脱离精算损失模型框架的通用数据科学、机器学习 pipeline 或量化研究 →
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data-scientist
```
、
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quantitative-researcher
```
仅涉及图表设计与仪表板制作的场景 →
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data-visualization
```
仅涉及资质路径与考试策略的场景 →
```
associate-actuary
```

Related skills

Need	Skill
Workpapers, triangles, exhibits, model I/O, analyst QA	`actuarial-analyst`
Sign-off, capital overview, governance memos	`actuary`
Appointed actuary / chief actuary regulatory framing	`appointed-chief-actuary`
ASA/FSO exam pathways and professional standards	`associate-actuary`
Assumption governance and enterprise change control	`assumption-setting`
P&C lines, underwriting, claims, and policy mechanics	`property-casualty-insurance`
Statistical/ML modeling beyond standard actuarial methods	`quantitative-researcher`
General ML and predictive pipelines	`data-scientist`
Charts, dashboards, and visual design	`data-visualization`

需求	技能
工作底稿、三角表、展示材料、模型输入输出、分析师质量检查	`actuarial-analyst`
签字确认、资本概览、管理备忘录	`actuary`
指定精算师/首席精算师的监管框架搭建	`appointed-chief-actuary`
ASA/FSO考试路径与专业标准	`associate-actuary`
假设管理与企业变更控制	`assumption-setting`
财产险产品线、核保、理赔及保单机制	`property-casualty-insurance`
超出标准精算方法的统计/机器学习建模	`quantitative-researcher`
通用机器学习与预测 pipeline	`data-scientist`
图表、仪表板与可视化设计	`data-visualization`

Core Workflows

核心工作流程

1. Problem framing (ASTAM-aligned)

1. 问题框架搭建（符合ASTAM标准）

Before fitting distributions:

Horizon — Short-term (annual or shorter); accident vs calendar year; prospective period for pricing
Random variables — Severity (X), frequency (N), aggregate (S=\sum X_i); clarify i.i.d. assumptions
Data grain — Claim-level vs policy-period; censoring/truncation (deductibles, limits)
Deliverable — Model spec, parameter estimates, diagnostics, business interpretation—not filing sign-off
Peer execution — Route spreadsheet builds and filing exhibits to
```
actuarial-analyst
```

See
references/astam_scope_and_principles.md
.

拟合分布前：

时间范围 — 短期（年度或更短）；事故年 vs 日历年度；定价的前瞻周期
随机变量 — 损失程度(X)、发生频率(N)、总损失(S=\sum X_i)；明确独立同分布假设
数据粒度 — 赔案级 vs 保单周期级；删失/截断（免赔额、赔偿限额）
交付成果 — 模型规格、参数估计、诊断结果、业务解读——而非申报签字文件
协作执行 — 将电子表格构建与申报展示材料转交
```
actuarial-analyst
```

参考
references/astam_scope_and_principles.md
。

2. Severity and frequency modeling

2. 损失程度与发生频率建模

Explore severity empirical tail; candidate families (exponential, gamma, lognormal, Pareto, generalized Pareto for tail)
Explore frequency dispersion; test Poisson vs negative binomial vs mixtures
Document moments, tail indices, and parameter stability across segments
State dependence assumptions (usually independence for standard compound model; flag if copula needed → escalate)
Summarize model selection criteria (AIC/BIC, Anderson–Darling, QQ plots)—not a single automatic pick

See
references/severity_and_frequency_models.md
.

探索损失程度的经验尾部；候选分布族（指数分布、伽马分布、对数正态分布、帕累托分布、用于尾部的广义帕累托分布）
探索发生频率的离散程度；检验泊松分布 vs 负二项分布 vs 混合分布
记录矩、尾部指数及各细分群体的参数稳定性
说明相关性假设（标准复合模型通常假设独立；若需Copula则升级处理）
总结模型选择标准（AIC/BIC、Anderson–Darling检验、QQ图）——并非单一自动选择结果

参考
references/severity_and_frequency_models.md
。

3. Aggregate and compound losses

3. 总损失与复合损失

Define compound model (S = X_1 + \cdots + X_N)
Apply normal approximation when conditions hold; state when it fails (heavy tail, low frequency)
Outline FFT and simulation approaches for discrete/continuous severity (conceptual steps)
Relate percentiles of (S) to risk measures and reinsurance layers (technical only)

See
references/aggregate_loss_models.md
.

定义复合模型(S = X_1 + \cdots + X_N)
在满足条件时应用正态近似；说明其失效场景（厚尾、低频率）
概述针对离散/连续损失程度的FFT与模拟方法（概念步骤）
将(S)的百分位数与风险度量及再保险层级关联（仅技术层面）

参考
references/aggregate_loss_models.md
。

4. Credibility and experience rating

4. 可信度与经验费率

Choose limited fluctuation, Bühlmann, or Bühlmann-Straub per homogeneity and data structure
Compute credibility weights (Z); define complement (manual, industry, prior)
Blend observed experience with complement for pure premium or loss ratio
Document heterogeneity across classes/years and structural parameters

See
references/credibility_and_experience_rating.md
.

根据同质性与数据结构选择有限波动、Bühlmann或Bühlmann-Straub方法
计算可信度权重(Z)；定义补充项（人工、行业、先验）
将观测经验与补充项结合，计算纯保费或损失率
记录不同类别/年度的异质性及结构参数

参考
references/credibility_and_experience_rating.md
。

5. Ratemaking and short-term reserving (math level)

5. 费率厘定与短期准备金计提（数学层面）

Pure premium indication: frequency × severity with documented adjustments
Loss ratio and on-level premium; trend to prospective period
Indicated change vs constraints; distinguish technical indication from implemented rate
Reserving: chain-ladder factor algebra, expected loss ratio method—link full triangle work to
```
actuarial-analyst
```

See
references/ratemaking_and_trend.md
.

纯保费指示值：发生频率×损失程度，并记录调整项
损失率与平准化保费；针对前瞻周期的趋势调整
指示性变动 vs 约束条件；区分技术指示值与实际执行费率
准备金计提：链梯法因子代数、预期损失率法——将完整三角表工作转交
```
actuarial-analyst
```

参考
references/ratemaking_and_trend.md
。

6. Estimation, diagnostics, and risk measures

6. 参数估计、诊断分析与风险度量

Fit via MLE (or method of moments where standard); report standard errors when available
Run goodness-of-fit and tail diagnostics; document limitations
Compute VaR and TVaR at stated confidence levels; interpret for capital layers (non-regulatory)
Package assumptions, alternatives, and sensitivity for actuary review

See
references/estimation_diagnostics_and_risk_measures.md
.

通过MLE（标准场景下也可使用矩估计法）拟合模型；若有可用值则报告标准误差
开展拟合优度检验与尾部诊断；记录局限性
在指定置信水平下计算VaR与TVaR；解读其对资本层级的影响（非监管层面）
整理假设、备选方案与敏感性分析结果，提交给精算师审核

参考
references/estimation_diagnostics_and_risk_measures.md
。

Deliverable standards

交付成果标准

Deliverable	Minimum content
Model specification	Random variables, independence, censoring/truncation, segment definition
Parameter table	Estimates, method, uncertainty, stability notes
Diagnostics	QQ/PP, GOF tests, tail plot, A/E if applicable
Business bridge	Pure premium, credibility blend, indicated change or reserve factor (math only)
Limitations	Data volume, tail extrapolation, regime change, outlier treatment

Label output as technical modeling support, not actuarial opinion, legal advice, or filed regulatory submission.

交付成果	最低内容要求
模型规格	随机变量、独立性、删失/截断、细分群体定义
参数表	估计值、方法、不确定性、稳定性说明
诊断结果	QQ/PP图、拟合优度检验、尾部图、适用情况下的实际/预期比值（A/E）
业务关联	纯保费、可信度混合结果、指示性费率变动或准备金因子（仅数学层面）
局限性	数据量、尾部外推、制度变更、异常值处理

将输出标注为技术建模支持，而非精算意见、法律建议或已提交的监管申报文件。

Assignment type matrix

任务类型矩阵

Trigger phrase	Primary workflow	Lead reference
severity model / tail behavior	Severity families and selection	`severity_and_frequency_models.md`
frequency model / negative binomial	Frequency and dispersion	`severity_and_frequency_models.md`
aggregate loss / compound distribution	Compound (S)	`aggregate_loss_models.md`
Bühlmann credibility	Credibility weights	`credibility_and_experience_rating.md`
experience rating / pure premium	Rating blend	`credibility_and_experience_rating.md`
ratemaking / trend / on-level	Indication math	`ratemaking_and_trend.md`
chain ladder / ELR (math)	Reserving formulas	`ratemaking_and_trend.md`
MLE / goodness-of-fit	Estimation and GOF	`estimation_diagnostics_and_risk_measures.md`
VaR / TVaR	Risk measures	`estimation_diagnostics_and_risk_measures.md`

触发短语	核心工作流程	主要参考文档
severity model / tail behavior	损失程度分布族与模型选择	`severity_and_frequency_models.md`
frequency model / negative binomial	发生频率与离散程度	`severity_and_frequency_models.md`
aggregate loss / compound distribution	复合模型(S)	`aggregate_loss_models.md`
Bühlmann credibility	可信度权重	`credibility_and_experience_rating.md`
experience rating / pure premium	费率混合计算	`credibility_and_experience_rating.md`
ratemaking / trend / on-level	费率指示值数学计算	`ratemaking_and_trend.md`
chain ladder / ELR (math)	准备金计提公式	`ratemaking_and_trend.md`
MLE / goodness-of-fit	参数估计与拟合优度检验	`estimation_diagnostics_and_risk_measures.md`
VaR / TVaR	风险度量	`estimation_diagnostics_and_risk_measures.md`

When to load references

参考文档加载场景

Scope, ASTAM alignment, principles →

references/astam_scope_and_principles.md

Severity and frequency →

references/severity_and_frequency_models.md

Aggregate and compound losses →
```
references/aggregate_loss_models.md
```

Credibility and experience rating →

references/credibility_and_experience_rating.md

Ratemaking, trend, reserving math →
```
references/ratemaking_and_trend.md
```

Estimation, GOF, VaR/TVaR →

references/estimation_diagnostics_and_risk_measures.md

范围、ASTAM对齐、原则 →

references/astam_scope_and_principles.md

损失程度与发生频率 →

references/severity_and_frequency_models.md

总损失与复合损失 →
```
references/aggregate_loss_models.md
```

可信度与经验费率 →

references/credibility_and_experience_rating.md

费率厘定、趋势调整、准备金计提数学 →
```
references/ratemaking_and_trend.md
```

参数估计、拟合优度、VaR/TVaR →

references/estimation_diagnostics_and_risk_measures.md