Credibility Theory Flashcards
7 cards from real Actuary Certification practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Credibility Theory flashcards as text
Under limited fluctuation credibility, approximately how many expected claims are needed for full credibility of claim frequency at 90% confidence with ±5% accuracy?
Answer: 1,082
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.
In the Bühlmann credibility premium P = Z × X̄ + (1−Z) × μ, the credibility factor Z equals:
Answer: n / (n + k)
Z = n/(n+k) is the Bühlmann credibility factor, where n is the number of observations and k = EVPV/VHM.
Under classical credibility, if full credibility requires n₀ = 1,082 claims and a risk has n = 271 claims, the partial credibility factor Z is:
Answer: 0.50
Using the square-root formula: Z = √(n/n₀) = √(271/1082) = √(0.25) = 0.50.
In the Bühlmann model, the parameter k is defined as:
Answer: EVPV / VHM
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.
The Expected Value of Process Variance (EVPV) in credibility theory is formally defined as:
Answer: E_Θ[Var(X|Θ)]
EVPV = E_Θ[Var(X|Θ)], the expected within-risk process variance averaged over the prior distribution of risk parameters.
The Variance of Hypothetical Means (VHM) in credibility theory is formally defined as:
Answer: Var_Θ[E(X|Θ)]
VHM = Var_Θ[E(X|Θ)], measuring how much the true risk means vary across different risks in the portfolio.
By the law of total variance, the total variance of a single observation X in the Bühlmann model equals:
Answer: EVPV + VHM
Var(X) = E[Var(X|Θ)] + Var(E[X|Θ]) = EVPV + VHM, by direct application of the law of total variance.