Actuary Certification Insurance Models 4

Question 1

Under the two-parameter Pareto distribution (Pareto II / Lomax), the mean excess loss function e(d) is:

Accepted Answer

(β + d) / (α − 1)

Answer

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.

Question 2

The Normal Power (NP) approximation is used to approximate:

Accepted Answer

The aggregate loss distribution using the first three moments

Answer

The NP approximation adjusts the normal approximation using skewness (third moment) to better capture the right tail of aggregate losses.

Question 3

In a compound Poisson model where S has Poisson(λ) claim counts and exponential(θ) severities, the moment generating function of S is:

Accepted Answer

exp(λ(Mx(t) − 1))

Answer

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.

Question 4

What distinguishes excess-of-loss (XL) per-occurrence reinsurance from per-aggregate (stop-loss) reinsurance?

Accepted Answer

XL applies to each individual claim; stop-loss applies to total period losses

Answer

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.

Question 5

Inflation at annual rate r shifts a loss distribution so that the limited expected value at u after t years becomes:

Accepted Answer

E[min(X, u(1+r)^t)]

Answer

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.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification Insurance Models 4