Question

Losses follow a Poisson frequency distribution with a mean of 2 per year. The amount of a loss is 1,2, or 3 with each having a probability of 1/3. Loss amounts are independent of the number of losses and from each other. An insurance policy covers all losses in a year subject to an annual aggregate deductible of 2. Calculate the expected claim payments for this insurance policy.

Answer 1

Solution

Let S denote aggregate losses before deductible.

E(S) = 2*2 = 4

f(0) = e^-2 (1) = 0.1353

f(1) = e^-2 (1/3) = 0.0902

E(S²) = 0*0.1353 + 1*(0.09022) + 2*(1-0.01353-0.0902) = 1.6392

expected claim = 4-1.6392 = 2.3608