Cramér–Lundberg model in risk theory
E933487
The Cramér–Lundberg model in risk theory is a classical stochastic model used in actuarial science to describe an insurer’s surplus over time, analyzing ruin probabilities based on premium income and random claim arrivals.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Cramér–Lundberg model | 0 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
actuarial model
ⓘ
risk model ⓘ stochastic process model ⓘ |
| aggregateClaimsProcess | compound Poisson process ⓘ |
| analyzes | probability of ruin ⓘ |
| appliesTo |
non-life insurance
ⓘ
property and casualty insurance ⓘ |
| assumes |
claims arrive according to a Poisson process
ⓘ
constant premium income rate ⓘ independence between claim sizes and claim arrival process ⓘ independent and identically distributed claim sizes ⓘ |
| coreConcept |
adjustment coefficient
ⓘ
finite-time ruin probability ⓘ net profit condition ⓘ safety loading ⓘ ultimate ruin probability ⓘ |
| describes | insurer surplus process ⓘ |
| field |
actuarial science
ⓘ
applied probability ⓘ risk theory ⓘ |
| hasAssumptionType | classical risk model assumptions ⓘ |
| hasComponent |
claim arrival process
ⓘ
claim size distribution ⓘ initial surplus ⓘ premium rate ⓘ surplus process ⓘ |
| hasVariant |
Cramér–Lundberg model with diffusion
NERFINISHED
ⓘ
Cramér–Lundberg model with investment income NERFINISHED ⓘ Cramér–Lundberg model with reinsurance NERFINISHED ⓘ |
| isBasisFor | many modern ruin theory extensions ⓘ |
| mathematicalFormulation | surplus equals initial capital plus premium income minus aggregate claims ⓘ |
| namedAfter |
Filip Lundberg
NERFINISHED
ⓘ
Harald Cramér NERFINISHED ⓘ |
| originatedIn | early 20th century ⓘ |
| relatedTo |
Gerber–Shiu function
NERFINISHED
ⓘ
collective risk model NERFINISHED ⓘ individual risk model ⓘ renewal risk model ⓘ |
| solutionMethod |
Laplace transform techniques
ⓘ
integro-differential equations ⓘ martingale methods ⓘ |
| timeParameter | continuous time ⓘ |
| typicalAssumptionOnClaims |
claim sizes have finite mean
GENERATED
ⓘ
claim sizes have finite variance GENERATED ⓘ |
| usedFor |
capital requirement assessment
ⓘ
premium calculation ⓘ risk management in insurance ⓘ solvency analysis ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.