Actuary Certification Insurance Models 2

Question 1

In the collective risk model, what does the aggregate loss S = X1 + X2 + ... + XN represent?

Accepted Answer

Sum of individual claim severities over a random number of claims

Answer

Total number of claims in a period

Answer

Average claim severity multiplied by exposure

Answer

Net premium income minus expenses

Question 2

Which distribution is used to model the time between successive claim arrivals in a Poisson process?

Accepted Answer

Exponential

Answer

Gamma

Answer

Weibull

Answer

Lognormal

Question 3

A stop-loss reinsurance treaty pays losses exceeding a retention d. The net stop-loss premium equals:

Accepted Answer

E[max(S − d, 0)]

Answer

E[S] − d

Answer

E[S − d]

Answer

P(S > d)

Question 4

The coefficient of variation (CV) of aggregate losses S is lower than the CV of individual claim severity X when:

Accepted Answer

There are many independent claims (large n)

Answer

The claim count N is deterministic

Answer

The claim count variance exceeds its mean

Answer

Claim severities are heavy-tailed

Question 5

Under the individual risk model, the total loss for a group of n independent policies is modeled as:

Accepted Answer

S = b1·I1 + b2·I2 + ... + bn·In where Ii are Bernoulli indicators

Answer

A compound Poisson distribution

Answer

The convolution of n Poisson random variables

Answer

A negative binomial aggregate

Question 6

What is the primary advantage of using the recursive (Panjer) formula for aggregate loss distributions?

Accepted Answer

It efficiently computes the aggregate distribution when (a,b,0) claim counts are combined with discrete severities

Answer

It applies only to exponential severity distributions

Answer

It avoids the need for moment generating functions

Answer

It provides closed-form solutions for all severity distributions

Question 7

In insurance pricing, the pure premium is calculated as:

Accepted Answer

Expected losses divided by earned exposure units

Answer

Expected losses divided by expected claim count

Answer

Gross premium minus expenses

Answer

Loss ratio multiplied by earned premium