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.
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.
01Qeyd
Actuarial mathematics at Actuarial and Quantitative Risk on the record.
Method recordSTEM method
- RêbazActuarial mathematics
- ParêzvanXetera aktuarî û hejmarî
- Applied inXetera aktuarî û hejmarî
- Dane3 inputs
- Checks3 validation steps
- Canonical pageSTEM Commons
02Serlêdan
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.
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.
Kontrol
- Typical annual hazard intensity (location)
- 1.00 intensity index
- Belavbûna nirxên tund (pîvan)
- 0.80 intensity index
- Tundiya ku nîvê nirxê tê de winda dibe
- 4.00 intensity index
- Belavbûna lawazî
- 0.55
- Para nirxê di nav şopa metirsî de
- 40%
- Standarda parastinê (heyama vegerê)
- 50 sal
Xwendin
- Windahiya salane ya navînî
- 0.51% of value
- Windahî di 1 ji 100 salan de
- 24.5% of value
- Windahî di 1 ji 250 salan de
- 28.4% of value
- Tundî di 1 ji 100 salan de
- 4.68 intensity index
Jimar, rêbaz û çavkanî
| Heyama vegerê (sal) | Intensity (intensity index) | Windahî (% ya nirxê) |
|---|---|---|
| 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 |
Rêbaz
- Metirsî: nirxên dawîn ên Gumbel Gumbel (1958), Statistics of Extremes, Columbia University Press
- Nazikiya lognormal (lawazî) FEMA (2003), HAZUS-MH Technical Manual
- Qada îhtîmala derbasbûnê û windahiya salane ya navînî Grossi and Kunreuther (2005), Catastrophe Modeling, Springer
- Bandora bendavê Di Baldassarre and others (2013), Socio-hydrology, HESS 17
- Pankeya nediyarîyê (Monte Carlo ya parametreyan) Spiegelhalter, Pearson and Short (2011), Visualising uncertainty about the future, Science 333
- Hesasiyeta yek-yek (tornado) Saltelli and others (2008), Global Sensitivity Analysis: The Primer, Wiley
Dane
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:
- Çem Natural Earth
- Dirêjahiyên bajarî Natural Earth
- Bajar Natural Earth
- Erdhejên M4.5+, hefteya borî (USGS) U.S. Geological Survey · register usgs.earthquake.summary-feeds
- Rêjeya baranê, nîv saeta dawîn (IMERG) NASA GPM IMERG Early · register nasa.gibs.context-live-layers
- Pêşbînî: herikîna çemê, 30 roj bi navber (GloFAS bi riya Open-Meteo) Open-Meteo.com (CC BY 4.0), Copernicus GloFAS · register open-meteo.public-pages
- Berfirehiya avakirî û niştecihbûnê, 2010 (HBASE, Landsat) CIESIN/Columbia, NASA SEDAC HBASE · register sedac.context-urban-layers
Li seranserê şeş stûnan, bi pêşengiya Nexus Consortium
- Ceribandin Labs
- Hatiye avakirin di Actuarial and Quantitative Risk in Foundry
- Tê ceribandin li Actuarial and Quantitative Risk in Universe
- Hatiye kodkirin di Darayî, sîgorta û aborî di Standards de
- Hatiye weşandin di Actuarial and Quantitative Risk in Reports
- Tê de tê dayîn Fakulteya Darayî û Aborî di Academy de
04Dane
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.
| Dane | Rol | Nîşan |
|---|---|---|
| Loss development triangles | Reserving | Statîstîkên weşandî |
| Exposure and policy data | Pricing | REPORTED |
| Mortality tables | Life valuation | TEXMÎNKIRÎ |
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.
| Return period | Annual probability | Gross loss | Net loss | Net, capital = 100 |
|---|---|---|---|---|
| 1 in 10 | 0.10 | 14 | 10 | 10 |
| 1 in 50 | 0.02 | 33 | 21 | 21 |
| 1 in 100 | 0.01 | 46 | 27 | 27 |
| 1 in 250 | 0.004 | 68 | 39 | 39 |
| Windahiya salane ya navînî | 3.1 | 2.2 | 2.2 |
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
06Erêkirin
How results are checked.
Assumptions are tested through experience studies and actual-versus-expected analysis. Independent actuarial review checks methods and results.
| Kontrol bikin | How it is done |
|---|---|
| Actual versus expected | Assumptions are compared with emerging experience |
| Peer review | Work is reviewed under professional standards |
| Hesasî | Key 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.
09Pirs
Pirs û bersiv.
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?
Çavdêrxaneya canonical method page lists every platform that applies it.
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Ji vê rûpelê delîl bidin.
rêzeya Pergalên Stratejîk 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.
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Agahî û pirs îro vekirî ne. Pirsek referansekê distîne û gava piştî wê dide nasîn; serlêdan, drav, veqetandina hesabkirinê û tomarkirin tenê dema ku tîm, mercên wê û kapasîteya vekolînê hebin vedibin.
Hiqûqî
Belgeyên hiqûqî.
Nexşe, dane û jimarên vê malperê ji bo çarçoveyê û agahiyên giştî têne nîşandan. Ew ne şîret, ne pêşbînî û ne hişyarî ne; sînorên agahiyê di Daxuyaniyên Berpirsiyariyê û Daxuyaniyên Daneyê de hatine diyarkirin.