Actuary Certification Loss Models Flashcards
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In loss models, which distribution is commonly used to model heavy-tailed claim severity due to its power-law tail?
Answer: Pareto distribution
The Pareto distribution has a power-law tail making it well-suited for modeling large, infrequent insurance claims with heavy tails.
The excess loss variable (X − d | X > d) for a deductible d is called the:
Answer: Mean excess loss function
The mean excess loss function e(d) = E[X − d | X > d] gives the expected claim payment above the deductible d, given that the loss exceeds d.
A compound Poisson frequency-severity model has aggregate loss S = X1 + X2 + ... + XN where N ~ Poisson(λ). The variance of S equals:
Answer: λ · E[X²]
For a compound Poisson distribution, Var(S) = λ · E[X²], which combines both frequency and the second moment of severity.
Which of the following is a member of the (a, b, 0) class of frequency distributions?
Answer: Negative Binomial
The Negative Binomial distribution belongs to the (a, b, 0) class because its probability ratios pk/pk−1 = a + b/k for k ≥ 1, alongside Poisson and Binomial.
The limited expected value E[X ∧ u] represents:
Answer: The expected loss capped at u
E[X ∧ u] = E[min(X, u)] is the limited expected value, representing the expected payment when losses are capped at a policy limit u.
Left-truncation of a loss variable at d (due to an ordinary deductible) means:
Answer: Losses below d are not observed at all
With left-truncation at d, losses below the deductible are never reported, so they are completely absent from the observed data.