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GRA · Actuarial and Quantitative Risk

Spatial financeWhere capital meets hazard, exposure and transition

Actuarial mathematics at Actuarial and Quantitative Risk

Actuarial mathematics turns experience, exposure and assumptions into premiums, reserves and capital. On this platform it is the core discipline, applied under professional standards and with the judgement and documentation those standards require.

پرسیارێک بنێرە Back to STEM foundation of Actuarial and Quantitative Risk
01تۆمارکردن

Actuarial mathematics at Actuarial and Quantitative Risk on the record.

Method recordSTEM method
  1. ڕێگاActuarial mathematics
  2. پارێزەرمەترسی ئەکچوەری و بڕی
  3. Applied inمەترسی ئەکچوەری و بڕی
  4. داتا3 inputs
  6. Canonical pageSTEM Commons
02بەکارهێنان

What actuarial mathematics does here.

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, methods and modelling and capital markets and investment, 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 the STEM Commons.

Reserving with development triangles

Chain ladder, Bornhuetter-Ferguson and stochastic methods project ultimate losses from development triangles, with the spread between methods reported as uncertainty.

Premium build-up

Expected losses, expenses, reinsurance costs and the cost of capital are combined into a technical premium, with each component documented.

Annuity valuation

Mortality tables and improvement assumptions are combined with discount rates to value annuities, with sensitivity to each assumption shown.

03Loss model

Loss exceedance, average annual loss and probable maximum loss.

The loss a portfolio in the footprint can expect per year and at the 1 in 100 and 1 in 250 levels that insurers and lenders price, from the same three blocks every catastrophe model uses. Teaching model with stated illustrative values, not a prediction.

کۆنترۆڵەکان

Typical annual hazard intensity (location)
1.00 intensity index
بڵاوبوونەوەی لێکەوتە توندەکان (پێوەر)
0.80 intensity index
توندییەک کە تێیدا نیوەی بەها لەدەست دەچێت
4.00 intensity index
بڵاوبوونەوەی لاوازی
0.55
بەشی بەها لە شوێنپێی مەترسیدەردا
40%
ستانداردی پاراستن (ماوەی گەڕانەوە)
50 ساڵ

خوێندنەوەکان

تێکڕای زیانی ساڵانە
0.51% of value
زیان لە 1 لە 100 ساڵدا
24.5% of value
زیان لە 1 لە 250 ساڵدا
28.4% of value
توندی لە 1 لە 100 ساڵدا
4.68 intensity index
ژمارە، ڕێگا و سەرچاوەکان
ماوەی گەڕانەوە (ساڵ)Intensity (intensity index)زیان (% ی بەها)
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

ڕێگاکان

  1. مەترسیدەری بەهای زۆرداری Gumbel Gumbel (1958)، Statistics of Extremes، Columbia University Press
  2. ناسکیی لۆگنۆرماڵ (لاوازی) FEMA (2003)، HAZUS-MH Technical Manual
  3. چەمکی ئەگەری تێپەڕبوون و تێکڕای زیانی ساڵانە Grossi و Kunreuther (2005)، Catastrophe Modeling، Springer
  4. کاریگەری بەربەست Di Baldassarre و ئەوانی دیکە (2013)، Socio-hydrology، HESS 17
  5. پەنجەی نادڵنیایی (مۆنتی کارلۆی پارامیتەر) Spiegelhalter, Pearson و Short (2011)، Visualising uncertainty about the future، Science 333
  6. هەستیاریی یەک-یەک (تۆرناد) Saltelli و ئەوانی دیکە (2008)، Global Sensitivity Analysis: The Primer، Wiley

داتا

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:

  • ڕووبارەکان Natural Earth
  • بەرینی شارەکان Natural Earth
  • شارەکان Natural Earth
  • بوومەلەرزەکانی M4.5+، هەفتەی ڕابردوو (USGS) U.S. Geological Survey · register usgs.earthquake.summary-feeds
  • ڕێژەی باران، نیو کاتژمێری ڕابردوو (IMERG) NASA GPM IMERG Early · register nasa.gibs.context-live-layers
  • پێشبینی ڕۆیشتنی ڕووبار، 30 ڕۆژ لەگەڵ مەودا (GloFAS لە ڕێگەی Open-Meteo) Open-Meteo.com (CC BY 4.0), Copernicus GloFAS · register open-meteo.public-pages
  • بەرینی دروستکراو و نیشتەجێبوون، 2010 (HBASE، Landsat) CIESIN/Columbia, NASA SEDAC HBASE · register sedac.context-urban-layers
Loss exceedance, average annual loss and probable maximum loss. Illustrative teaching model: it runs on the values set by the controls, not on measured data. Methods: Gumbel extreme-value hazard (Gumbel (1958), Statistics of Extremes, Columbia University Press); Lognormal fragility (vulnerability) (FEMA (2003), HAZUS-MH Technical Manual); Exceedance-probability curve and average annual loss (Grossi and Kunreuther (2005), Catastrophe Modeling, Springer).

لە ناو شەش کۆڵەکەکەدا، بە سەرپەرشتیی Nexus Consortium

04داتا

What the method consumes.

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 the source register.

داتاڕۆڵناونیشان
Loss development trianglesReservingئامارە بڵاوکراوەکان
Exposure and policy dataPricingREPORTED
Mortality tablesLife valuationمەزەندەکراو
05Exposure, loss and capital

What it means for exposure, loss and capital.

The exposure, loss, scenario and capital views a risk officer, supervisor or ministry of finance would ask for, with the frameworks they report against. Structures follow supervisory and actuarial practice. Values are illustrative: never prices, ratings or advice.

Exposure and loss at return periods

How losses from Actuarial mathematics at Actuarial and Quantitative Risk grow with severity, gross and net of reinsurance, against capital.

1 in 101 in 501 in 1001 in 250grossnet of reinsurance800
Return periodAnnual probabilityGross lossNet lossNet, capital = 100
1 in 100.10141010
1 in 500.02332121
1 in 1000.01462727
1 in 2500.004683939
تێکڕای زیانی ساڵانە3.12.22.2
Illustrative loss index for a example portfolio (capital = 100): the exceedance-probability form insurers and supervisors read. Not data on any institution, not a price or a rating.
NGFS climate scenarios · Network for Greening the Financial SystemIFRS S2 Climate-related Disclosures · ISSBTCFD recommendations · Financial Stability Board TCFDPrinciples for the effective management of climate-related financial risks · Basel Committee on Banking Supervision
06پشتڕاستکردنەوە

How results are checked.

Assumptions are tested through experience studies and actual-versus-expected analysis. Independent actuarial review checks methods and results.

بپشکنەHow it is done
Actual versus expectedAssumptions are compared with emerging experience
Peer reviewWork is reviewed under professional standards
هەستیاریKey assumptions are varied and effects reported

Historical experience may not reflect emerging or correlated risks. Long-tail liabilities are sensitive to assumptions about future trends.

07Connections

Topics that rely on this method.

08Stewardship

Who maintains the method.

Actuarial and Quantitative Risk stewards actuarial mathematics for the Consortium and reviews how it is applied across platforms.

Canonical page: Actuarial mathematics

09پرسیارەکان

پرسیار و وەڵام.

What are the limits of actuarial mathematics in this field?
Historical experience may not reflect emerging or correlated risks. Long-tail liabilities are sensitive to assumptions about future trends.
How are results checked?
Assumptions are tested through experience studies and actual-versus-expected analysis. Independent actuarial review checks methods and results.
Are the values on this page real?
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.
Where else is this method applied?
ئەو canonical method page lists every platform that applies it.
Reportsبەشداربە

لەم لاپەڕەیەوە بەڵگە پێشکەش بکە.

Reports 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.

Global Risks Allianceمەترسی ئەکچوەری و بڕیڕێگا و تەکنیکیئامادەیی دارایی و بیمە

هەرگیز داتای کەسی، وردەکاریی هەستیاری ژێرخان یان هیچ شتێک مەنێرە کە مافی بڵاوکردنەوەت نییە. بەشدارییەک پێش بەکارهێنان پێداچوونەوەی بۆ دەکرێت؛ ناردنی ماف نابەخشێت بە نووسەرایەتی یان بەڕێوەبردنی ڕاگەیاندن، و پاڵپشتی دارایی هەرگیز دۆزینەوەیەک ناکڕێت.

مەترسی ئەکچوەری و بڕی

Bring an exposure or capital question to the Alliance.

زانیاری و پرسیار ئەمڕۆ کراوەن. پرسیارێک ژمارەی ئاماژەی پێدەدرێت و هەنگاوی دواتر دیاری دەکات؛ داواکاری، پارەدان، تەرخانکردنی کۆمپیوتەر و تۆمارکردن تەنیا کاتێک دەکرێنەوە کە تیم، مەرج و توانای پێداچوونەوەیان هەبێت.

Propose a readiness pilot بینینی هەموو ڕێگاکانی پەیوەندی
یاسایی

نەخشە، داتا و وێنەکانی ئەم ماڵپەڕە بۆ ناوەڕۆک و زانیاریی گشتی پیشان دراون. ئامۆژگاری، پێشبینی یان ئاگادارکردنەوە نین؛ سنوورەکانی زانیارییەکە لە ڕەتکردنەوەی بەرپرسیارێتی و ئاگاداریی داتادا دەستنیشان کراون.