GCRI · Mathematics, statistics and data
Actuarial mathematics
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. Actuarial and Quantitative Risk stewards this page for the Nexus Consortium.
01Contents
Actuarial mathematics in six parts.
In this dossier6 parts
- 01The methodWhat actuarial mathematics covers
- 02Reference practiceActuarial mathematics is governed by professional and supervisory standards
- 03In systemic risk workPricing risk that is changing
- 04Applied inPlatforms that apply this method
- 05StewardshipWho maintains this page
- 06SourcesWhere this page’s references lead
02The method
What actuarial mathematics covers.
- 01
Core methods
loss distribution modelling; credibility theory; reserving methods; mortality and morbidity modelling; risk aggregation; catastrophe pricing.
- 02
Data and instruments
claims histories; exposure and policy data; mortality tables; catastrophe model outputs; economic assumptions.
- 03
Validation
Assumptions are tested through experience studies and actual-versus-expected analysis. Independent actuarial review checks methods and results.
- 04
Limits
Historical experience may not reflect emerging or correlated risks. Long-tail liabilities are sensitive to assumptions about future trends.
- 05
Use in risk decisions
Actuarial methods determine whether risks can be insured and at what cost. They help assess accumulation of correlated losses across portfolios and regions.
03Reference practice
Actuarial mathematics is governed by professional and supervisory standards.
| Reference | What it sets |
|---|---|
| IAIS ICPs | Insurance supervision |
| Actuarial professional standards | Practice standards of actuarial bodies |
| Catastrophe model frameworks | Hazard, vulnerability and financial modules |
04Process
How the process runs.
Process
Actuarial mathematics: Catastrophe model pipeline
Catastrophe models usually have hazard, vulnerability, exposure and financial modules, and produce loss tables, average annual loss, exceedance curves, PML and TVaR.
01 Hazard
- 01Event catalogueDataset · Model developerThe hazard module holds a large catalogue of simulated events that represents a wide range of plausible scenarios.
- 03Hazard moduleModel · Model developerFor each event the hazard module gives the local hazard intensity that the vulnerability module reads.
02 Exposure and damage
- 02ExposureDataset · Programme ownerThe exposure module houses the portfolio data, such as location-specific information.
- 04Vulnerability moduleModel · Model developerThe vulnerability module quantifies the expected damage to the exposures from an event.
03 Financial
- 05Financial moduleModel · Programme ownerThe financial module calculates losses from all event scenarios. Ground-up, gross and net losses differ as shown below.
- 06Event loss tableDataset · Programme ownerAn event loss table lists each event with its annual occurrence probability and its loss for the portfolio.
- 07Year loss tableDataset · Programme ownerSome models also sample simulated years from event losses. This outline does not describe their format.
04 Metrics
- 08Exceedance probability curvesModel · Programme ownerThe occurrence curve gives the chance that the largest loss in a year exceeds an amount. The aggregate curve does so for the sum of losses.
- 09AAL, PML and TVaRModel · Programme ownerAverage annual loss sums event probability times loss. PML is one point on the occurrence curve.
05 Use of results
- 10Use of resultsDecision · Programme ownerThe tail metrics are used when considering a portfolio’s exposure and the level of catastrophe reinsurance an insurer requires.
Outline of an external standard or method, from its public sources. It describes what the framework says, not a record of any run. It does not show that Nexus or any partner performs, certifies or approves a step. A gate is a step of the method, never a Nexus approval.
05In systemic risk work
Pricing risk that is changing.
Actuarial methods price and reserve for risk using historical experience. When hazards change, experience understates future losses. Integration of forward-looking hazard science with actuarial methods is the interface the Global Centre for Risk and Innovation (GCRI) contributes to.
- Adjust experience for trend.
- Combine catastrophe models with experience.
- No investment advice is given.
07Stewardship
Who maintains this page.
Actuarial and Quantitative Risk stewards actuarial mathematics: it keeps this description current and reviews how the method is applied across the platforms.
08Sources
Where this page’s references lead.
The bodies and documents this page is read against. Status and editions change; each link goes to the issuing body.
09Questions
Questions and answers.
Why does one institution host every method page?
GCRI hosts the STEM Commons so that each method has one canonical description. Platforms link to it rather than repeat it, which keeps definitions consistent.
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Write to the integrity concern form with the passage and the reason.
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