Questions and Problems 1. An insurer sells a very large number of policies to people with the following loss distribution: $100,000 with probability 0.005 $ 60,000 with probability 0.010 Loss = $ 20,000 with probability 0.020 $ 10,000 with probability 0.05 $ 0 with probability 0.915 a. Calculate the expected claim cost per policy. b. Assume claims are paid one year after premiums are received and that the in- terest rate is 6 percent. Calculate the dis- counted expected claim cost per policy. c. Assume that the only administrative cost is the cost of processing an application, which equals $100 per policy, and that the fair profit loading is $50. What is the fair premium? 2. Redo problem 1, but include the expected cost of loss adjustment expenses (the cost of processing claims), assuming that loss ad- justment expenses equal 12 percent of losses and are paid at the same time that claims are paid. 3. Redo problem 1 with the following loss distribution: $ 2,000,000 with probability 0.001 $ 1,000,000 with probability 0.005 200,000 with probability 0.010 100,000 with probability 0.020 0 with probability 0.964 Loss = $ $ $ Chapter 8 Insurance Pricing 1 4. Suppose an insurer estimates that an expo- sure has the following loss distribution: $600,000 with probability 0.01 Loss = $100,000 with probability 0.02 $ 30,000 with probability 0.03 S 0 with probability 0.94 Claim payments are not expected to be paid until one year after the premium is received. If the interest rate is 5 percent, what is the discounted expected claim cost? 5. Redo problem 4 assuming a 8 percent inter- est rate. 6. Redo problem 4 assuming claim payments are not made until two years after the pre- mium is received, 7. Based on your answers to problems through 6, make general statements abou the effect of interest rates and the claims tai on insurance premiums. 8. You have been hired to prepare a report ex amining whether gender should be outlawe as a rating factor for all insurance. Summa rize your main arguments for and against. 9. Chapter 5 explained how fixed premium in surance ontracts cause insurers to bear th risk that losses will be greater than e pected. Explain why this might not be true capital shocks affect insurance prices. 10. Given the existence of an underwriting c cle, when is the best time for individuals businesses to have to buy insurance? Wh is the worst time?

1. An insurer sells a very large number of policies to people with the following loss distribution: $100,000 with probability 0.005 S 60,000 with probability 0.010 Loss =$20,000 with probability 0.020 \$ 10,000 with probability 0.05 \$ 0 with probability 0.915 a. Calculate the expected claim cost per policy. b. Assume claims are paid one year after premiums are received and that the interest rate is 6 pereent. Calculate the discounted expected claim cost per policy. c. Assume that the only administrative cost is the cost of processing an application, which equals $100 per policy, and that the fair profit loading is $50. What is the fair premium? 2. Redo problem 1, but include the expected cost of loss adjustment expenses (the cost of processing claims), assuming that loss adjustment expenses equal 12 percent of losses and are paid at the same time that claims are paid. 3. Redo problem 1 with the following loss distribution: $2,000,000 with probability 0.001 $1,000,000 with probability 0.005 Loss =$200,000 with probability 0.010 \$ 100,000 with probability 0.020 4. Suppose an insurer estimates that an exposure has the following loss distribution: $600,000 with probability 0.01 Loss =$100,000 with probability 0.02 \$ 30,000 with probability 0.03 S 0 with probability 0.94 Claim payments are not expected to be paid until one year after the premium is received If the interest rate is 5 pereent, what is the discounted expected claim cost? 5. Redo problem 4 assuming a 8 percent interest rate. 6. Redo problem 4 assuming claim payment ate not made until two years after the pre mium is reccived. 7. Based on your answers to problems through 6 , make general statements abou the effect of interest rates and the claims tai on insurance premiums. 8. You have been hired to prepare a report ex amining whether gender should be outlawe as a tating factor for all insurance. Summa rize your main arguments for and against. 9. Chapter 5 explained how fixed premium it surance contracts cause insurers to bear th risk that losses will be greater than e pected. Explain why this might not be true capital shocks affect insurance prices. 10. Given the existence of an underwriting c cle, when is the best time for individuals businesses to have to buy insurance? Wh is the worst time