Question

n insurance portfolio consists of two homogeneous groups of clients; N i, (i = 1 , 2) denotes the number of claims occurred in the ith group in a fixed time period. Assume that the r.v.'s N 1, N 2 are independent and have Poisson distributions, with expected values 200 and 300, respectively.

The amount of an individual claim in the first group is a r.v. equal to either 10 or 20 with respective probabilities 0.3 and 0.7, while the amount of an individual claim in the second group equals 20 or 30 with respective probabilities 0.1 and 0.9.

Let N be the total number of claims, and let S be the total aggregate claim.

Find E { S } and V a r { S }.

(Hint: Compute E { Y i } and E { Y i 2 } proceeding from the result of Question 10 and use Propositions 1-2 that we proved in class regarding E { S } and V a r { S } in the case where N is a Poisson r.v.)

Answer 1

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