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

S is the aggregate loss formed by summing N individual claim amounts, where N is a random claim count variable.

Question 2

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

Accepted Answer

Exponential

Answer

Inter-arrival times in a Poisson process are exponentially distributed with the same rate parameter λ.

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

The stop-loss premium is the expected value of the excess loss above the retention, E[max(S−d,0)].

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

By the law of large numbers, pooling many independent claims reduces relative variability, lowering the CV of S compared to X.

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

The individual model sums fixed benefit amounts bi scaled by Bernoulli claim indicators Ii for each policy.

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