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
Under the two-parameter Pareto distribution (Pareto II / Lomax), the mean excess loss function e(d) is:
Answer: (β + d) / (α − 1)
For a two-parameter Pareto with parameters α and β, e(d) = (β + d)/(α−1), an increasing linear function of d indicating a heavy tail.
The Normal Power (NP) approximation is used to approximate:
Answer: The aggregate loss distribution using the first three moments
The NP approximation adjusts the normal approximation using skewness (third moment) to better capture the right tail of aggregate losses.
In a compound Poisson model where S has Poisson(λ) claim counts and exponential(θ) severities, the moment generating function of S is:
Answer: exp(λ(Mx(t) − 1))
The MGF of a compound Poisson S is Ms(t) = exp(λ(Mx(t)−1)) where Mx(t) is the MGF of the severity distribution.
What distinguishes excess-of-loss (XL) per-occurrence reinsurance from per-aggregate (stop-loss) reinsurance?
Answer: XL applies to each individual claim; stop-loss applies to total period losses
Per-occurrence XL reimburses the cedant for the amount of each single loss above the retention, while stop-loss applies to the aggregate over a period.
Inflation at annual rate r shifts a loss distribution so that the limited expected value at u after t years becomes:
Answer: E[min(X, u(1+r)^t)]
Inflation multiplies each loss by (1+r)^t, equivalent to deflating the limit to u/(1+r)^t, or equivalently E[min(inflated X, u)] = E[min(X, u/(1+r)^t)]·(1+r)^t.
The variance of aggregate losses under the collective model is:
Answer: E[N]·Var[X] + Var[N]·(E[X])²
By the law of total variance, Var[S] = E[N]·Var[X] + Var[N]·(E[X])², decomposing into severity and frequency components.
Which actuarial concept measures the expected loss for an insurer net of a proportional reinsurance cession of fraction α?
Answer: (1−α)·E[S]
Under quota share at cession rate α, the cedant retains fraction (1−α) of total losses, so net expected loss is (1−α)·E[S].