Frequency and severity modelling
Generalised linear models relate claim frequency and severity to risk factors, with offsets for exposure, so the contribution of each factor and its uncertainty can be read and reviewed.
GRA · Insurance Nexus
空间金融资本与危害、风险暴露和转型的交汇之处
保险中的概率与统计
Probability and statistics provide the language of insurance: frequency and severity, dependence, credibility and uncertainty. They make assumptions explicit, test them against experience, and show how much confidence any estimate of loss deserves, from a single portfolio’s claim frequency to a national estimate of how many households are uninsured.
02申请
What probability and statistics does here.
Probability and statistics provide the mathematical framework for describing uncertainty and learning from data. They underpin estimation, testing and prediction in every risk discipline. In insurance and catastrophe, climate and hazards and health and biosecurity, statistical methods quantify the likelihood and uncertainty of losses across interconnected 系统. They make the evidence behind risk decisions explicit and reproducible. The canonical description is on STEM Commons.
Bayesian updating of assumptions
Prior assumptions from industry or benchmark data are updated with an insurer’s own experience, giving posterior estimates that state how far the data have moved the assumption.
Survey design for protection gaps
Household surveys on insurance take-up are designed and weighted so that estimates of uninsured shares represent the population, and their sampling error is reported with them.
03损失模型
损失超越、年均损失和可能最大损失。
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
- 典型年度危害强度（所在地）
- 1.00 强度指数
- 极端值的扩散（尺度）
- 强度指数 0.80
- 损失一半价值时的强度
- 4.00 强度指数
- 脆弱性的离散程度
- 0.55
- 危害足迹中的价值占比
- 40%
- 防护标准（重现期）
- 50 年
读数
- 年均损失
- 占价值的 0.51%
- 百年一遇（1/100）的损失
- 占价值的 24.5%
- 250 年一遇（1/250）的损失
- 占价值的 28.4%
- 百年一遇（1/100）的强度
- 强度指数 4.68
数字、方法与来源
| 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 |
方法
- Gumbel 极值危害 Gumbel (1958), Statistics of Extremes, Columbia University Press
- 对数正态易损性（脆弱性） FEMA (2003), HAZUS-MH Technical Manual
- 超越概率曲线与年均损失 Grossi and Kunreuther (2005), Catastrophe Modeling, Springer
- 堤防效应 Di Baldassarre and others (2013), Socio-hydrology, HESS 17
- 不确定性扇形图（参数蒙特卡罗） Spiegelhalter, Pearson and Short (2011), Visualising uncertainty about the future, Science 333
- 单因素敏感性（龙卷风图） Saltelli and others (2008), Global Sensitivity Analysis: The Primer, Wiley
数据
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:
- 河流 Natural Earth
- 城市范围 Natural Earth
- 城市 Natural Earth
- 过去一周 M4.5+ 地震（USGS） 美国地质调查局 · 登记 usgs.earthquake.summary-feeds
- 降雨率，最近半小时（IMERG） NASA GPM IMERG Early · 登记 nasa.gibs.context-live-layers
- 河流流量预报，30 天及范围（GloFAS via Open-Meteo） Open-Meteo.com（CC BY 4.0）、Copernicus GloFAS · 登记 open-meteo.public-pages
- 建成区与居民点范围，2010 年（HBASE，Landsat） CIESIN/Columbia、NASA SEDAC HBASE · 登记 sedac.context-urban-layers
贯穿六大支柱，由 Nexus Consortium 牵头
04数据
该方法使用的输入。
Datasets and records used by probability and statistics 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 |
|---|---|---|
| Claims and exposure records | Model fitting | 已报告 |
| Industry benchmarks | Priors and comparison | 估算 |
| Household and enterprise surveys | Take-up and gap estimation | 观测 |
| Supervisory statistical returns | Market aggregates | 已发布统计 |
05风险暴露、损失与资本
What probability and statistics in insurance means for exposure, loss and capital.
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。
各重现期的风险暴露与损失
How losses from probability and statistics 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 |
NGFS 气候情景 · 央行与监管机构绿色金融网络IFRS S2 气候相关披露 · ISSBTCFD 建议 · 金融稳定理事会 TCFD有效管理气候相关金融风险的原则 · 巴塞尔银行监管委员会
06验证
结果如何核查。
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
| 核查 | 如何开展 |
|---|---|
| Out-of-sample validation | Models are fitted on one period or segment and tested on another; only test performance is reported |
| Residual diagnostics | Residuals are inspected for structure the model has missed, such as trends or clustering |
| Sensitivity to assumptions | Independence, distribution and sampling assumptions are varied and the effect on the result is stated |
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
08管理责任
由谁维护该方法。
系统科学与建模 stewards probability and statistics for the Consortium and reviews how it is applied across platforms.
09已关联
本页在整个联合体中通向何处。
10问题
问题与解答。
What are the limits of probability and statistics in this field?
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
结果如何核查？
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
本页面上的数值是真实的吗？
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
该方法还应用于何处？
维持社会运转的各个 规范方法页面 列出应用该方法的每个平台。
报告贡献
从本页贡献证据。
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.
全球风险联盟（Global Risks Alliance）Insurance Nexus金融与保险准备度全球部门风险与韧性
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法律
法律文件。
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