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.
- 01In briefThe short answer
- 02The methodWhat actuarial mathematics covers
- 03Reference practiceActuarial mathematics is governed by professional and supervisory standards
- 04In systemic risk workPricing risk that is changing
- 05Applied inPlatforms that apply this method
- 06StewardshipWho maintains this page
- 07Key termsTerms used on this page
GCRI · Institution · service level R0
The short answer.
Actuarial mathematics applies probability, statistics and financial theory to measure and price contingent risks, particularly in insurance and pensions. Actuarial methods determine whether risks can be insured and at what cost. In the Nexus Consortium, Actuarial and Quantitative Risk stewards its canonical page, and 4 other platforms apply it, including Insurance Nexus and Institutional Funds Nexus.
Financial centres and urban exposure in Middle East and North Africa.
The cities where people, assets and financial activity concentrate, shown for Middle East and North Africa as an example geography for this subject.
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.
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 |
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 GCRI contributes to.
- Adjust experience for trend.
- Combine catastrophe models with experience.
- No investment advice is given.
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.
Terms used on this page.
Each term as this page uses it. Where a standard-setting body defines the term, the wording follows that body.
| Term | Definition |
|---|---|
| Chain ladder method | A reserving method that projects ultimate claims from a development triangle using the average growth between successive development periods. |
| Bornhuetter-Ferguson method | A reserving method that blends an expected loss ratio with reported experience, giving more weight to experience as claims mature. |
| Credibility | The weight given to a portfolio's own experience against a wider benchmark, rising with the volume and stability of its data. |
| Incurred but not reported | Reserves for claims that have occurred but have not yet been reported to the insurer. |
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.
Where this page leads across the Consortium.
- Actuarial mathematics in insuranceGRAApplied in Insurance Nexus.
- Actuarial mathematics for pension fundsGRAApplied in Institutional Funds Nexus.
- Actuarial mathematics for reinsurance and catastropheGRAApplied in Reinsurance and Catastrophe.
- Actuarial mathematics for disaster risk financeGRAApplied in Disaster Risk Finance.
- Actuarial mathematics at Actuarial and Quantitative RiskGRAApplied in Actuarial and Quantitative Risk.
Questions and answers.
Why does one institution host every method page?
How do I suggest a correction to a method page?
Around GCRI.
Start with an enquiry.
The current service level is R0: information and enquiries. An enquiry receives a reference and names the next step; applications, payments, compute allocations and registrations open only when their team, terms and review capacity exist.