Actuary Certification Actuary Certification Loss Models 1

Question 1

In loss models, which distribution is commonly used to model heavy-tailed claim severity due to its power-law tail?

Accepted Answer

Pareto distribution

Answer

The Pareto distribution has a power-law tail making it well-suited for modeling large, infrequent insurance claims with heavy tails.

Question 2

The excess loss variable (X − d | X > d) for a deductible d is called the:

Accepted Answer

Mean excess loss function

Answer

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.

Question 3

A compound Poisson frequency-severity model has aggregate loss S = X1 + X2 + ... + XN where N ~ Poisson(λ). The variance of S equals:

Accepted Answer

λ · E[X²]

Answer

For a compound Poisson distribution, Var(S) = λ · E[X²], which combines both frequency and the second moment of severity.

Question 4

Which of the following is a member of the (a, b, 0) class of frequency distributions?

Accepted Answer

Negative Binomial

Answer

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.

Question 5

The limited expected value E[X ∧ u] represents:

Accepted Answer

The expected loss capped at u

Answer

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.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification Actuary Certification Loss Models 1