An employer buys an insurance for his employees.The mean number of claims coming

Question

An employer buys an insurance for his employees.The mean number of claims coming from the whole group of employees is 50, the standard deviation is 10. The individual loss has a mean of 4 (units of money) and a variance of 2. The insurance company imposes a deductible of 50 for the whole portfolio. Assuming that the distribution of the aggregated loss is closely approximated by a -distribution, find the probability that the company will pay more than 200 units. An employer buys an insurance for his employees.The mean number of claims coming from the whole group of employees is 50, the standard deviation is 10. The individual loss has a mean of 4 (units of money) and a variance of 2. The insurance company imposes a deductible of 50 for the whole portfolio. Assuming that the distribution of the aggregated loss is closely approximated by a -distribution, find the probability that the company will pay more than 200 units. An employer buys an insurance for his employees.The mean number of claims coming from the whole group of employees is 50, the standard deviation is 10. The individual loss has a mean of 4 (units of money) and a variance of 2. The insurance company imposes a deductible of 50 for the whole portfolio. Assuming that the distribution of the aggregated loss is closely approximated by a -distribution, find the probability that the company will pay more than 200 units.

Explanation / Answer

mean number of claims (N) coming from the whole group of employees is 50 and standard deviation is 10

E(N) =50, Var(N) =100

whereas individual loss has a mean of 4 (units of money) and a variance of 2

E(X) = 4, Var(X) =2

Aggregated loss mean and variance is

E(S) =200, Var(S)= 4*100+2500*2 = 5400

Aggregated loss is closely approximated by a -distribution then the probability that the company will pay more than 200 units is

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