Actuary Certification Insurance Models 3 — Questions and Answers
Question 1: Which of the following is a key property of the Poisson distribution that makes it useful in claim count modeling?
- Its mean always exceeds its variance
- Its mean equals its variance (Correct answer)
- It is defined on all real numbers
- It always produces overdispersed data
Correct answer: Its mean equals its variance
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:
- All losses above a fixed retention
- A fixed fraction α of every loss (Correct answer)
- Losses between two attachment points
- The difference between actual and expected losses
Correct answer: A fixed fraction α of every loss
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:
- E[min(X,d)] / E[X] (Correct answer)
- E[X − d | X > d]
- 1 − F(d)
- d / E[X]
Correct answer: E[min(X,d)] / E[X]
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?
- Collective risk model
- Individual risk model
- Credibility model with Bühlmann-Straub (Correct answer)
- Compound frequency model
Correct answer: Credibility model with Bühlmann-Straub
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:
- max(X − d, u)
- min(X, u + d) − d (Correct answer)
- u for all X > d
- X − d for all X > 0
Correct answer: min(X, u + d) − d
The payment is min(X, u+d) − d, capped at u, since the insurer covers the loss above d up to the maximum u.
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:
- Decreases toward 0
- Remains at 0.5 regardless
- Increases toward 1 (Correct answer)
- Equals the prior mean
Correct answer: Increases toward 1
As data volume grows, Z approaches 1, meaning the estimate relies almost entirely on the insured's own observed experience.
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?
- Exponential
- Lognormal
- Weibull (Correct answer)
- Pareto
Correct answer: Weibull
The Weibull distribution has a flexible hazard function; with shape parameter τ < 1 it is decreasing, τ > 1 increasing, and it can model bathtub shapes with mixtures.
Actuary Certification Insurance Models 3
Which of the following is a key property of the Poisson distribution that makes it useful in claim count modeling?