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.
GRA · Actuarial and Quantitative Risk
Spatial financeWhere capital meets hazard, exposure and transition
Probability and statistics for actuarial and quantitative risk
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.
01Qeyd
Probability and statistics for actuarial and quantitative risk on the record.
Method recordSTEM method
- RêbazÎhtîmal û statîstîk
- ParêzvanZanista pergalan û modelkirin
- Applied inXetera aktuarî û hejmarî
- Dane3 inputs
- Checks3 validation steps
- Canonical pageSTEM Commons
02Serlêdan
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 pergalan. They make the evidence behind risk decisions explicit and reproducible. The canonical description is on the STEM Commons.
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.
03Çavdêrî bike
Tail fit.
The screen a team would use to follow this method: its measures, states and decisions. Names are examples and values are illustrative.
Tail fit
Actuarial and quantitative risk · Probability and statistics · Run R-1415
Shape parameter uncertainGRA · Actuarial and Quantitative Risk
Return level curve
Method card
- Rêbaz
- Îhtîmal û statîstîk
- Nêzîkatî
- peaks over threshold
- Threshold
- 93th percentile
- Nîşan
- MODELKIRÎ
Parameters
generalised Pareto fit
| Shape ξ | 0.10 | 0.01 | 0.43 | heavy tail if above zero |
| Scale σ | 1.6 | 0.9 | 7.1 | units of the variable |
| Exceedances | 132 | declustered |
04Dane
What the method consumes.
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 the source register.
| Dane | Rol | Nîşan |
|---|---|---|
| Claims and exposure records | Model fitting | REPORTED |
| Industry benchmarks | Priors | TEXMÎNKIRÎ |
| Mortality data | Life models | Statîstîkên weşandî |
05Loss 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
06Erêkirin
How results are checked.
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
| Kontrol bikin | How it is done |
|---|---|
| Out-of-sample validation | Models are tested on data not used for fitting |
| Residual diagnostics | Residuals are inspected for structure |
| Assumption sensitivity | Distributional 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.
07Exposure, 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 probability and statistics for 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
08Connections
Topics that rely on this method.
09Stewardship
Who maintains the method.
Zanista pergalan û modelkirin stewards probability and statistics for the Consortium and reviews how it is applied across platforms.
10Girêdayî
Ev rûpel li ser Konsorsiyûmê te ber bi kû ve dibe.
11Pirs
Pirs û bersiv.
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.
How are results checked?
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
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.
rêzeya Pergalên StratejîkTevkarî bike
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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Xetera aktuarî û hejmarî
Bring an exposure or capital question to the Alliance.
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.