Actuary Certification Insurance Models 3

Question 1

Which of the following is a key property of the Poisson distribution that makes it useful in claim count modeling?

Accepted Answer

Its mean equals its variance

Answer

Its mean always exceeds its variance

Answer

It is defined on all real numbers

Answer

It always produces overdispersed data

Question 2

A proportional (quota share) reinsurance arrangement means the reinsurer pays:

Accepted Answer

A fixed fraction α of every loss

Answer

All losses above a fixed retention

Answer

Losses between two attachment points

Answer

The difference between actual and expected losses

Question 3

The loss elimination ratio (LER) at deductible d for a loss random variable X is defined as:

Accepted Answer

E[min(X,d)] / E[X]

Answer

E[X − d | X > d]

Answer

1 − F(d)

Answer

d / E[X]

Question 4

Which model assumes that the parameter of an insured's loss distribution itself follows a distribution across the portfolio?

Accepted Answer

Credibility model with Bühlmann-Straub

Answer

Collective risk model

Answer

Individual risk model

Answer

Compound frequency model

Question 5

A policy with a policy limit u and deductible d pays the insured at most:

Accepted Answer

min(X, u + d) − d

Answer

max(X − d, u)

Answer

u for all X > d

Answer

X − d for all X > 0

Question 6

In experience rating, the credibility-weighted estimate blends the insured's own experience with the class mean. As the volume of own experience increases, the credibility factor Z:

Accepted Answer

Increases toward 1

Answer

Decreases toward 0

Answer

Remains at 0.5 regardless

Answer

Equals the prior mean

Question 7

Which severity distribution is characterized by a hazard rate that increases then decreases (bathtub shape), making it useful for modeling equipment failure in insurance contexts?

Accepted Answer

Weibull

Answer

Exponential

Answer

Lognormal

Answer

Pareto