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

Constant at β/α

Answer

α·d / β

Answer

(β − d) / α

Question 2

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

Accepted Answer

The aggregate loss distribution using the first three moments

Answer

The claim count distribution for small portfolios

Answer

The severity distribution of individual losses

Answer

Reinsurance pricing via simulation

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

λ/(λ − t)

Answer

e^(λt) / (1 − θt)

Answer

1 / (1 − λθt)

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

XL applies only to liability lines; stop-loss to property

Answer

XL always has unlimited coverage; stop-loss is always capped

Answer

XL is cheaper than stop-loss in all market conditions

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

E[min(X, u)] · (1+r)^t

Answer

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

Answer

E[min(X, u)] + u·r·t

Question 6

The variance of aggregate losses under the collective model is:

Accepted Answer

E[N]·Var[X] + Var[N]·(E[X])²

Answer

E[N]·Var[X]

Answer

Var[N]·Var[X]

Answer

E[N²]·E[X²]

Question 7

Which actuarial concept measures the expected loss for an insurer net of a proportional reinsurance cession of fraction α?

Accepted Answer

(1−α)·E[S]

Answer

α·E[S]

Answer

E[S] − α·Var[S]

Answer

E[S]/(1+α)