Insurance Models 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 Insurance Models flashcards as text
The Cramér-Lundberg ruin theory model assumes claims arrive as a Poisson process and premiums flow continuously. The adjustment coefficient R satisfies:
Answer: λM_X(R) = λ + cR
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.
In a Bühlmann credibility model, the credibility factor Z = n/(n+k) where k is:
Answer: The ratio of expected process variance to structural variance
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.
The limited expected value E[min(X, u)] for an exponential distribution with mean θ equals:
Answer: θ(1 − e^{−u/θ})
For X ~ Exp(θ), E[min(X,u)] = θ(1 − e^{−u/θ}), which approaches θ = E[X] as u→∞.
Under a franchise deductible d (as opposed to a straight deductible), the insurer pays:
Answer: X in full when X > d, zero otherwise
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.
Which property of a severity distribution ensures that the mean excess loss function e(d) is constant for all d?
Answer: Memorylessness of the exponential distribution
The memoryless property of the exponential distribution implies e(d) = θ for all d, a constant equal to the mean.
A risk is said to be 'super-additive' in the context of insurance if:
Answer: The risk measure of the combined portfolio exceeds the sum of individual risk measures
Super-additivity means ρ(X+Y) > ρ(X) + ρ(Y); this can occur with certain non-subadditive risk measures and strongly dependent risks.
An insurer uses simulation to estimate the 99th percentile of aggregate losses. To reduce the variance of this estimate, which technique is most appropriate?
Answer: Applying importance sampling or stratified sampling
Variance reduction techniques like importance sampling oversample the tail region, producing more precise estimates of high percentiles with fewer simulations.