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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Cramér–Lundberg model in risk theory canonical | 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]
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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.
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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.
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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.
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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
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Cramér–Lundberg model in risk theory Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.