Actuary Certification Insurance Models 5

Question 1

The Cramér-Lundberg ruin theory model assumes claims arrive as a Poisson process and premiums flow continuously. The adjustment coefficient R satisfies:

Accepted Answer

λM_X(R) = λ + cR

Answer

The adjustment coefficient R is the positive root of λM_X(R) = λ + cR (the Lundberg equation), where c is premium rate and λ is claim rate.

Question 2

In a Bühlmann credibility model, the credibility factor Z = n/(n+k) where k is:

Accepted Answer

The ratio of expected process variance to structural variance

Answer

k = v/a where v is the expected value of process variance (EVPV) and a is the variance of hypothetical means (VHM), the structural variance.

Question 3

The limited expected value E[min(X, u)] for an exponential distribution with mean θ equals:

Accepted Answer

θ(1 − e^{−u/θ})

Answer

For X ~ Exp(θ), E[min(X,u)] = θ(1 − e^{−u/θ}), which approaches θ = E[X] as u→∞.

Question 4

Under a franchise deductible d (as opposed to a straight deductible), the insurer pays:

Accepted Answer

X in full when X > d, zero otherwise

Answer

A franchise deductible pays the full loss X (not X−d) once X exceeds the threshold d, unlike an ordinary deductible which pays X−d.

Question 5

Which property of a severity distribution ensures that the mean excess loss function e(d) is constant for all d?

Accepted Answer

Memorylessness of the exponential distribution

Answer

The memoryless property of the exponential distribution implies e(d) = θ for all d, a constant equal to the mean.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification Insurance Models 5