Actuary Certification Credibility Theory 1

Question 1

Under limited fluctuation credibility, approximately how many expected claims are needed for full credibility of claim frequency at 90% confidence with ±5% accuracy?

Accepted Answer

1,082

Answer

Applying n₀ = (z/r)² = (1.645/0.05)² ≈ 1,082, where z = 1.645 for 90% confidence and r = 0.05 for ±5% accuracy.

Question 2

In the Bühlmann credibility premium P = Z × X̄ + (1−Z) × μ, the credibility factor Z equals:

Accepted Answer

n / (n + k)

Answer

Z = n/(n+k) is the Bühlmann credibility factor, where n is the number of observations and k = EVPV/VHM.

Question 3

Under classical credibility, if full credibility requires n₀ = 1,082 claims and a risk has n = 271 claims, the partial credibility factor Z is:

Accepted Answer

0.50

Answer

Using the square-root formula: Z = √(n/n₀) = √(271/1082) = √(0.25) = 0.50.

Question 4

In the Bühlmann model, the parameter k is defined as:

Accepted Answer

EVPV / VHM

Answer

k = EVPV/VHM (Expected Value of Process Variance divided by Variance of Hypothetical Means); a larger k means more observations are needed to earn credibility.

Question 5

The Expected Value of Process Variance (EVPV) in credibility theory is formally defined as:

Accepted Answer

E_Θ[Var(X|Θ)]

Answer

EVPV = E_Θ[Var(X|Θ)], the expected within-risk process variance averaged over the prior distribution of risk parameters.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification Credibility Theory 1