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GRA · Insurance Nexus

空间金融资本与危害、风险暴露和转型的交汇之处

面向保险尾部的极值理论

Extreme value theory gives the tail of the loss distribution its shape: how large a rare event loss may be, how losses accumulate in a bad year, and how uncertain those estimates become beyond the record. Capital, reinsurance and catastrophe pricing all rest on it.

提出咨询 Back to STEM foundation of Insurance Nexus
01目录

Extreme value theory for insurance tails in five parts.

方案5 个步骤
  1. 01申请What extreme value theory and tail risk does here
  2. 02数据该方法使用的输入
  3. 03验证结果如何核查
  4. 04关联依赖该方法的主题
  5. 05管理责任由谁维护该方法
02申请

What extreme value theory and tail risk does here.

Extreme value theory and 尾部风险 study the behaviour of rare, high-impact events. They provide methods to estimate the magnitude and frequency of extremes beyond the range of observed data. In insurance and catastrophe, climate and hazards and health and biosecurity, extreme value methods set design levels and capital buffers for rare events. Tail dependence analysis reveals when extremes in different 系统 tend to occur together. The canonical description is on STEM Commons.

Large-loss pricing for excess layers

Losses above a threshold are fitted with a generalised Pareto distribution to price excess-of-loss reinsurance layers, with the threshold choice and its effect on the layer price shown.

Tail measures for solvency capital

Loss distributions are extended into the tail to estimate 风险价值 and tail value at risk at regulatory confidence levels, with parameter uncertainty and alternative fits reported.

Tail dependence across lines and perils

Copulas and multivariate extreme value models examine whether extreme losses in different lines, regions or asset classes tend to occur together, which governs how much diversification credit is defensible.

03空间金融

风险暴露、危害与超越概率曲线。

哪些地方在严重年份造成损失，以及损失向再保险蔓延的程度。示意性设计数值。

气旋和地震带下的沿海风险暴露，以及它所产生的损失曲线。示意性设计值，并非模型输出或价格。
04数据

该方法使用的输入。

Datasets and records used by extreme value theory and 尾部风险 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
Large-loss historiesTail fitting观测
Industry catastrophe loss recordsEvent severity估算
巨灾模型 event setsSynthetic tail extension模型估算
Hazard maxima such as wind speed and rainfallHazard tail behaviour观测
05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

Insurance · Extreme value theory for insurance · Run R-7661

Shape parameter uncertainGRA · Insurance Nexus

Return level curve

方法卡

方法
极值理论与尾部风险
方法
peaks over threshold
Threshold
90th percentile
标签
模型估算

参数

generalised Pareto fit

Shape ξ0.22−0.030.45heavy tail if above zero
Scale σ2.71.06.9units of the variable
Exceedances88declustered
Tail fit: the screen’s structure, terms and states for Insurance.示例名称和示意数值；是设计方案，并非记录或实时系统。
06验证

结果如何核查。

Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.

核查如何开展
Threshold stabilityTail parameters are estimated across a range of thresholds and the choice is justified by stability plots
Goodness of fit in the tailFits are judged on tail behaviour, not overall fit, using quantile plots and out-of-sample large losses
Parameter uncertaintyConfidence intervals for return-period losses are reported, by bootstrap or profile likelihood
Indexation and stationarityLosses are brought to a common basis for inflation and exposure, and trends are tested before fitting

Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.

07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 uses. Teaching model with stated illustrative values, not a prediction. The map on this page shows The Gulf of Mexico coast; the model itself is not tied to a place.

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

08关联

依赖该方法的主题。

09孪生与级联模拟器

Trace a shock in extreme value theory for insurance tails to the balance sheet.

Assembled from the Nexus Standards area profile 保险与再保险: the shocks it names, the 系统 and sectors that carry the loss, the controls that dampen it and the data that observe it. Pick an initiating shock and step through the cascade to see which exposures it reaches and where losses could concentrate. The Map view places the run on an example geography with open data. Every weight is a stated assumption. An exercise, not a forecast, a valuation, a rating or investment advice. To model a place of your own choosing, open the full System Builder.

灾害

  • 热带气旋
  • 地震
  • 冰塞洪水
  • 野火
  • Storm surge （在下游引发）
  • Intense rainfall （在下游引发）
  • 河流洪水（在下游引发）
  • Flash flood (set off downstream)
  • 危险海浪（在下游引发）
  • 大范围停电（在下游引发）
  • 大规模流离失所（在下游引发）
  • 沿海洪水（在下游引发）
  • Aftershock sequence (set off downstream)
  • Fault surface rupture (set off downstream)
  • Soil liquefaction (set off downstream)
  • Slope slide (set off downstream)
  • Rockfall (set off downstream)
  • Tsunami (set off downstream)

控制措施

  • NS-0 章程与原则
  • NS-3 风险记录 UNI（语法、旧编码对照、分配机构）
  • NS-9 情境 UNI（部署、实例、计划实例）
  • NS-10 政策和条款（机器可读的义务：定义、约束、评估和执行）
  • NS-11 验证与监测（证据、证明、零信任符合性观测）
  • NS-14 符合性及与外部标准的对照
  • NRS-F3 保险、巨灾风险与保护缺口
  • NRS-H113 危害类别：金融体系脆弱性（NHS-1 soc.financial-system）
  • NRS-U17 宇宙 platform profile: Insurance Nexus
  • NRS-H71 危害类别：深时与宇宙灾难（NHS-1 planet.deep-time）
  • NRS-H65 危害类别：超越行星边界（NHS-1 planet.boundary）
  • NRS-F8 参数化与指数型风险转移

观测

  • OECD Data Explorer (incl. Creditor Reporting System, insurance and pension statistics) (listed for reference)
  • Insurance statistics (listed for reference)
  • USGS earthquake GeoJSON summary feeds (listed for reference)
  • Direct economic loss attributed to disasters in relation to global gross domestic product (GDP)
  • Direct economic loss attributed to disasters in relation to global gross domestic product
  • (a) Number of commercial bank branches per 100,000 adults and (b) number of automated teller machines (ATMs) per 100,000 adults

示例地理范围

  • 西欧：152 个六边形网格
  • 过去半小时降雨率（IMERG），NASA GIBS
  • 今夜夜间灯光与停电（VIIRS 昼夜波段），NASA GIBS
  • 穿透云层的地表水，30 m（OPERA DSWx-S1 雷达），NASA GIBS
  • Carbon monoxide, smoke transport (AIRS), NASA GIBS
10管理责任

由谁维护该方法。

再保险与巨灾 stewards extreme value theory and 尾部风险 for the Consortium and reviews how it is applied across platforms.

Canonical page: Extreme value theory and tail risk

11风险暴露、损失与资本

What extreme value theory for insurance tails 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 extreme value theory for insurance tails 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
12已关联

本页在整个联合体中通向何处。

13问题

问题与解答。

What are the limits of extreme value theory and tail risk in this field?
Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.
结果如何核查？
Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.
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

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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