Cramér–Lundberg model in risk theory

E933487

actuarial model risk model stochastic process model

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.

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All labels observed (4)

Label	Occurrences
Cramér–Lundberg model in risk theory canonical	1
Cramér–Lundberg model with diffusion	1
Cramér–Lundberg model with investment income	1
Cramér–Lundberg model with reinsurance	1

How this entity was disambiguated

This entity first appeared as the object of triple T11560423 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Cramér–Lundberg model in risk theory
Context triple: [Harald Cramér, knownFor, Cramér–Lundberg model in risk theory]

A. Tirpitz risk theory
Tirpitz risk theory was a pre–World War I German naval strategy asserting that building a powerful battle fleet would deter Britain by making any conflict at sea too risky for the Royal Navy.
B. Modern Probability Theory and Its Applications
"Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
C. Khinchin–Pollaczek formula
The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
D. Act on Non-Life Insurance Rating Organizations of Japan
The Act on Non-Life Insurance Rating Organizations of Japan is a Japanese law that regulates the establishment and operation of rating organizations that calculate and provide standard premium rates for non-life insurance.
E. Limit Laws for Sums of Independent Random Variables
Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Cramér–Lundberg model in risk theory
Target entity description: 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.

A. Tirpitz risk theory
Tirpitz risk theory was a pre–World War I German naval strategy asserting that building a powerful battle fleet would deter Britain by making any conflict at sea too risky for the Royal Navy.
B. Modern Probability Theory and Its Applications
"Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
C. Khinchin–Pollaczek formula
The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
D. Act on Non-Life Insurance Rating Organizations of Japan
The Act on Non-Life Insurance Rating Organizations of Japan is a Japanese law that regulates the establishment and operation of rating organizations that calculate and provide standard premium rates for non-life insurance.
E. Limit Laws for Sums of Independent Random Variables
Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
F. None of above. chosen

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 ⓘ linked to: Cramér–Lundberg model in risk theory Cramér–Lundberg model with investment income ⓘ linked to: Cramér–Lundberg model in risk theory Cramér–Lundberg model with reinsurance ⓘ linked to: Cramér–Lundberg model in risk theory
isBasisFor	many modern ruin theory extensions ⓘ
mathematicalFormulation	surplus equals initial capital plus premium income minus aggregate claims ⓘ
namedAfter	Filip Lundberg ⓘ Harald Cramér ⓘ
originatedIn	early 20th century ⓘ
relatedTo	Gerber–Shiu function ⓘ collective risk model ⓘ individual risk model ⓘ renewal risk model ⓘ
solutionMethod	Laplace transform techniques ⓘ integro-differential equations ⓘ martingale methods ⓘ
timeParameter	continuous time ⓘ
typicalAssumptionOnClaims	claim sizes have finite mean ⓘ claim sizes have finite variance ⓘ
usedFor	capital requirement assessment ⓘ premium calculation ⓘ risk management in insurance ⓘ solvency analysis ⓘ