Question

You are given an automobile collision coverage with a 500 deductible. The number of paid claims np follows a nb(b,r) distribution with b = 0.4 and r = 0.5. The ground-up loss sizes follow a pareto(a,0) distribution with a = 1 and 0 = 100. Determine the deductible needed in order to reduce the variance of the number of payments to 0.2?

Answer 1

To reduce the variance of the number of payments to 0.2, the deductible needed in automobile collision coverage can be found using the negative binomial and Pareto distributions.

Step-by-step explanation:

To reduce the variance of the number of payments to 0.2, we need to determine the deductible needed for the automobile collision coverage. Given that the number of paid claims follows a negative binomial distribution with parameters b = 0.4 and r = 0.5, and the ground-up loss sizes follow a Pareto distribution with parameter a = 1 and 0 = 100, we can calculate the deductible. The deductible needed can be found by determining the loss size at which the cumulative distribution function (CDF) of the Pareto distribution equals 0.2. The deductible would be the difference between this loss size and 100.