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
The full credibility standard for pure premiums requires more expected claims than for claim frequency alone because:
Answer: Pure premiums depend on both frequency and severity, adding severity variance to total variance
Pure premiums combine frequency and severity, so total variance includes both sources; the standard becomes n₀ = (z/r)²(1 + CV²_S) where CV_S is the severity coefficient of variation.
If claim severity follows an exponential distribution (CV_S = 1.0), the full credibility standard for pure premiums at 90% confidence with ±5% accuracy requires approximately:
Answer: 2,164 expected claims
n₀ = 1,082 × (1 + CV²_S) = 1,082 × (1 + 1²) = 2,164 expected claims for full credibility of pure premiums.
Within a given risk (conditional on its parameter Θ), successive annual observations X₁, X₂, ..., Xₙ in the Bühlmann model are:
Answer: Conditionally independent and identically distributed given Θ
Given Θ, observations are conditionally i.i.d.; unconditional positive correlation between same-risk observations arises only from the unknown shared Θ, not from serial dependence.
The exact Bayesian credibility estimate equals the Bühlmann linear credibility estimate when:
Answer: The likelihood is from the exponential family with a conjugate prior (e.g., Poisson/Gamma, Normal/Normal)
For exponential family likelihoods paired with conjugate priors, the Bayesian posterior mean is linear in the observed data, making it identical to the Bühlmann estimate.
A credibility premium is computed as P = Z × 250 + (1−Z) × 200 = 230. What is the credibility factor Z?
Answer: 0.60
Setting Z(250) + (1−Z)(200) = 230 gives 200 + 50Z = 230, so 50Z = 30, thus Z = 0.60.
For a portfolio of risks, estimated EVPV = 400 and estimated VHM = 500. What is Bühlmann's k?
Answer: 0.80
k = EVPV/VHM = 400/500 = 0.80; this low k means credibility builds quickly (fewer observations needed).
Using k = 0.80 from the portfolio above, a risk with n = 4 years of data has X̄ = 140 and the portfolio mean μ = 110. What is the Bühlmann credibility premium?
Answer: 135.0
Z = 4/(4 + 0.80) = 4/4.80 ≈ 0.833; premium = 0.833(140) + 0.167(110) = 116.67 + 18.33 ≈ 135.0.