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

For a Poisson distribution, E[N] = Var[N] = λ, which is the equidispersion property central to many insurance models.

Question 2

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

Accepted Answer

A fixed fraction α of every loss

Answer

Under quota share, both losses and premiums are shared in fixed proportion α between cedant and reinsurer.

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

LER(d) = E[min(X,d)] / E[X], measuring the proportion of expected losses eliminated by the deductible.

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

Bühlmann-Straub credibility models a heterogeneous portfolio where each insured has a parameter drawn from a structural (prior) distribution.

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

The payment is min(X, u+d) − d, capped at u, since the insurer covers the loss above d up to the maximum u.

Actuary Certification Practice Test