GRA · Insurance Nexus
空间金融资本与危害、风险暴露和转型的交汇之处
Actuarial mathematics is the core discipline of insurance: it turns claims experience, exposure and assumptions into premiums, reserves and capital. On this platform it frames how expected loss and its uncertainty are estimated, and where professional judgement and standards set the boundaries.
Actuarial mathematics applies probability, statistics and financial theory to measure and price contingent risks, particularly in insurance and pensions. It determines reserves and premiums for uncertain future obligations. In insurance and catastrophe, climate and hazards and health and biosecurity, actuarial methods determine whether risks can be insured and at what cost. They help assess accumulation of correlated losses across portfolios and regions. The canonical description is on STEM Commons.
Paid and incurred claims are arranged by origin and development period, and chain ladder, Bornhuetter-Ferguson and stochastic methods project ultimate losses, with the spread between methods reported as part of the uncertainty.
A portfolio’s own claims experience is blended with a wider benchmark in proportion to its credibility, so small books are not priced on noise and large books are not priced on someone else’s experience.
Graduated mortality rates are combined with improvement scales fitted to population and insured data, and the resulting annuity values are tested against alternative scales to show their sensitivity.
团队遵循该方法时会使用的界面：其指标、状态与决策。名称为示例，数值仅作示意。
Insurance · Actuarial mathematics in insurance · Run R-7651
generalised Pareto fit
| Shape ξ | 0.07 | −0.06 | 0.41 | heavy tail if above zero |
| Scale σ | 2.6 | 0.9 | 7.3 | units of the variable |
| Exceedances | 57 | declustered |
Datasets and records used by actuarial mathematics on this platform, with the role each plays and the label its values carry. Sources are listed in 来源登记册.
| 数据 | 角色 | 标签 |
|---|---|---|
| Loss development triangles | Reserving | 已发布统计 |
| Policy and exposure data | Pricing and experience rating | 已报告 |
| Mortality and morbidity tables | Life and health assumptions | 估算 |
| 巨灾模型 event loss tables | Catastrophe load and accumulation | 模型估算 |
| Price and inflation indices | Trend and discounting | 已发布统计 |
处于覆盖范围内的投资组合每年预期损失，以及保险公司和贷款机构定价所依据的 1/100 和 1/250 水平下的预期损失，均来自每个 巨灾模型 所用的同样三个模块。教学模型，所用数值为注明的示意值，并非预测。
控制措施
读数
| 重现期（年） | 强度（强度指数） | 损失（占价值的 %） |
|---|---|---|
| 1 | 0.09 | 0.00 |
| 2 | 1.27 | 0.00 |
| 4 | 1.91 | 0.00 |
| 7 | 2.47 | 0.00 |
| 13 | 3.00 | 0.00 |
| 24 | 3.51 | 0.00 |
| 44 | 4.02 | 0.00 |
| 82 | 4.53 | 23.55 |
| 154 | 5.03 | 26.44 |
| 287 | 5.53 | 28.87 |
| 536 | 6.03 | 30.88 |
| 1,000 | 6.53 | 32.53 |
The model runs on the teaching values set by the controls. To calibrate it for a place, read it against these admitted layers and series, which this page’s map can draw:
贯穿六大支柱，由 Nexus Consortium 牵头
Assumptions are tested through experience studies and actual-versus-expected analysis. Independent actuarial review checks methods and results.
| 核查 | 如何开展 |
|---|---|
| Actual versus expected | Emerging experience is compared with assumed claims each period, and persistent deviations trigger review of the assumption |
| Reserve back-testing | Past reserve estimates are compared with later ultimate losses to measure adequacy and bias |
| Independent actuarial review | Methods and assumptions are reviewed by an actuary not involved in the work, against the applicable professional standards |
| Sensitivity reporting | Key assumptions are varied and the effect on premiums, reserves and capital is reported beside the central estimate |
Historical experience may not reflect emerging or correlated risks. Long-tail liabilities are sensitive to assumptions about future trends.
风险官、监管者或财政部会要求的风险暴露、损失、情景和资本视图，以及它们据以报告的框架。结构遵循监管和精算实务。数值为说明性：绝非价格、评级或建议。
How losses from actuarial mathematics in insurance grow with severity, gross and net of reinsurance, against capital.
| 重现期 | 年概率 | 总损失 | 净损失 | 净额，资本 = 100 |
|---|---|---|---|---|
| 1/10（10 年一遇） | 0.10 | 14 | 10 | 10 |
| 1/50（50 年一遇） | 0.02 | 33 | 21 | 21 |
| 1/100（100 年一遇） | 0.01 | 46 | 27 | 27 |
| 1/250（250 年一遇） | 0.004 | 68 | 39 | 39 |
| 年均损失 | 3.1 | 2.2 | 2.2 |
精算与量化风险 stewards actuarial mathematics for the Consortium and reviews how it is applied across platforms.
报告 is the Consortium’s quarterly publication. What you know about this subject can become evidence, a case or a correction in the next edition, credited to you and published under CC BY 4.0 where it is your own work.
切勿发送个人数据、敏感基础设施细节或您无权分享的任何内容。贡献在使用前会经过审查；发送贡献不赋予署名权或编辑权，赞助也绝不能换取研究结论。
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