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GRA · 精算与量化风险

空间金融资本与危害、风险暴露和转型的交汇之处

面向精算与量化风险的概率与统计

Probability and statistics provide the language of quantitative risk: distributions, estimation, dependence, testing and uncertainty. On this platform they underpin loss modelling, credibility, mortality and validation, and show how much confidence each estimate deserves.

提出咨询 Back to STEM foundation of Actuarial and Quantitative Risk
01登记

Probability and statistics for actuarial and quantitative risk on the record.

方法记录STEM 方法
  1. 方法概率与统计
  3. 应用于精算与量化风险
  4. 数据3 inputs
  6. 规范页面STEM 公共资源
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, methods and modelling and capital markets and investment, 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.

Generalised linear models in pricing

Claim frequency and severity are related to risk factors with exposure offsets, so each factor’s effect and uncertainty can be reviewed.

Bayesian credibility

Prior assumptions from industry data are updated with own experience, giving posterior estimates that show how far the data moved the prior.

Goodness-of-fit testing

Fitted distributions are tested with formal statistics and quantile plots, with attention to fit in the tail where it matters most.

03监测

Tail fit.

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。

Tail fit

Actuarial and quantitative risk · Probability and statistics · Run R-1415

Shape parameter uncertainGRA · 精算与量化风险

Return level curve

方法卡

方法
概率与统计
方法
peaks over threshold
Threshold
93th percentile
标签
模型估算

参数

generalised Pareto fit

Shape ξ0.100.010.43heavy tail if above zero
Scale σ1.60.97.1units of the variable
Exceedances132declustered
Tail fit: the screen’s structure, terms and states for Actuarial and quantitative risk.示例名称和示意数值；是设计方案，并非记录或实时系统。
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 recordsModel fitting已报告
Industry benchmarksPriors估算
Mortality dataLife models已发布统计
05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 %）
10.090.00
21.270.00
41.910.00
72.470.00
133.000.00
243.510.00
444.020.00
824.5323.55
1545.0326.44
2875.5328.87
5366.0330.88
1,0006.5332.53

方法

  1. Gumbel 极值危害 Gumbel (1958), Statistics of Extremes, Columbia University Press
  2. 对数正态易损性（脆弱性） FEMA (2003), HAZUS-MH Technical Manual
  3. 超越概率曲线与年均损失 Grossi and Kunreuther (2005), Catastrophe Modeling, Springer
  4. 堤防效应 Di Baldassarre and others (2013), Socio-hydrology, HESS 17
  5. 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
  6. 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
损失超越概率、年均损失和可能最大损失。示意性教学模型：它依据控件设定的数值运行，而不是实测数据。方法：Gumbel 极值危害（Gumbel（1958），Statistics of Extremes，Columbia University Press）；对数正态脆弱性曲线（FEMA（2003），HAZUS-MH Technical Manual）；超越概率曲线与年均损失（Grossi 和 Kunreuther（2005），Catastrophe Modeling，Springer）。

贯穿六大支柱，由 Nexus Consortium 牵头

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 validationModels are tested on data not used for fitting
Residual diagnosticsResiduals are inspected for structure
Assumption sensitivityDistributional assumptions are varied and effects reported

Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.

07风险暴露、损失与资本

What it 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 for actuarial and quantitative risk grow with severity, gross and net of reinsurance, against capital.

1/10（10 年一遇）1/50（50 年一遇）1/100（100 年一遇）1/250（250 年一遇）总额扣除再保险后的净额800
重现期年概率总损失净损失净额，资本 = 100
1/10（10 年一遇）0.10141010
1/50（50 年一遇）0.02332121
1/100（100 年一遇）0.01462727
1/250（250 年一遇）0.004683939
年均损失3.12.22.2
一个示例投资组合的示意性损失指数（资本 = 100）：保险公司和监管机构所读的超越概率形式。并非任何机构的数据，也非价格或评级。
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
08关联

依赖该方法的主题。

09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.

Canonical page: Probability and statistics

10已关联

本页在整个联合体中通向何处。

11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）精算与量化风险方法与技术金融与保险准备度

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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