A portfolio consists of three homogeneous groups. The number of clients in each

Question

A portfolio consists of three homogeneous groups. The number of clients in each group, n_i, and the probabilities of loss events for each group, r_i, i = 1, 2, 3, are given in the following table: (a) Find p_n bar and the parameter lambda of the approximating Poisson distribution. (b) For the number of claims N, estimate P(N = 15) and P(N lessthanorequalto 15). (For calculations, it makes sense to use software.) (c) If the data is annual data, how often, on the average, can you expect less than 16 claims a year?

Explanation / Answer

Solution:

a. = niri

= 231*0.01 + 124*0.05 + 347*0.03

= 18.92

pn = 18.92/(231 + 124 + 347) = 0.02695

b. Using Excel,

=POISSON(15,18.92,FALSE)

= 0.066

P (N = 15) = 0.066

Using Excel,

=POISSON(15,18.92,TRUE)

P (N 15) = 0.2200

c. 15 claims or less happen approximately once each five years.

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