Actuary Certification Actuary Certification Loss Models

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

Normal distribution

Answer

Binomial distribution

Answer

Uniform distribution

Question 2

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

Accepted Answer

Mean excess loss function

Answer

Limited expected value

Answer

Left-censored variable

Answer

Stop-loss transform

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

λ · E[X]

Answer

λ · Var(X)

Answer

λ² · E[X²]

Question 4

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

Accepted Answer

Negative Binomial

Answer

Lognormal

Answer

Weibull

Answer

Pareto

Question 5

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

Accepted Answer

The expected loss capped at u

Answer

The expected loss above the policy limit u

Answer

The variance of X truncated at u

Answer

The deductible at level u

Question 6

Left-truncation of a loss variable at d (due to an ordinary deductible) means:

Accepted Answer

Losses below d are not observed at all

Answer

Losses below d are set to zero in the data

Answer

Losses above d are censored

Answer

The policy pays only losses exactly equal to d