An insurance company has a portfolio of 100 policyholders. 25 of the policyholders have loss distributions...

An insurance company has a portfolio of 100 policyholders. 25 of the policyholders have loss distributions with mean 50and variance 10, and 75 of the policyholders have loss distributions with mean 10and variance 30. Assuming the insurance company charges all policyholders the same premium, what premium should the company charge so that there is a 95% chance that aggregate claims will be less than the total premium collected?

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Expert Solution

Expected loss of all policyholders = 25 * 50 + 75 * 10 = 2000

Variance of loss of all policyholders = 25 * 10 + 75 * 30 = 2500

Standard deviation of loss of all policyholders = = 50

By Central limit theorem, we can assume that Loss of all policyholders X ~ N(2000 , 50)

Let k be the total premium charged to all 100 policyholders such that,

P(X < k) = 0.95

=> k =

=> k = 2000 + 1.645 * 50 = $2082.25

Premium per policyholders = 2082.25 / 100 = $20.82

The company should charge $20.82 per policyholder so that there is a 95% chance that aggregate claims will be less than the total premium collected.

orchestra answered 1 year ago

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