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An insurer sells a very large number of policies to people who each have the following identical loss (claims) distribution
Loss/claim Probability
100,000 .005
60,000 .010
20,000 .020
10,000 .050
0 .915
1 A. Calculate the Expected claim cost per person.
1 B. Assume claims are paid out 1 year after premiums are received and the discount rate is 6%. Calculate the Present value of expected claim cost
1 C. Assume that the only administrative cost is the cost of processing an application which is $100 per policy and that the fair profit loading is $50. Calculate the Fair premium .
Redo problem 1, but include the expected costs of lost adjustment expenses (the cost of processing claims) assuming that loss adjustment expenses equal 12% of losses and are paid at the time that claims are paid.
2 A. Expected loss adjustment expenses =
2 B. Present value of expected loss adjustment expenses =
2 C. Fair premium =
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The solution explains the concepts very well using the example in the question. All the steps are clearly explained and outlined. The answer is very easy to understand and can be followed along with anyone who has a basic understanding of the subject. Overall, an excellent response to the question.
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1A.
Expected Claim cost per person = 100,000*.005 + 60,000*.01 + 20,000*.02 + 10,000*.05 + 0*.915 = 2,000
1B.
Present Value of the Expected Claims = 2,000/1.06 = ...
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