Insurance Policy

1 Five of ten people earn $0, four earn $100, and one loses $100. What is the expected payoff? What is the variance of the payoff?

2 You have a 50 percent chance of making $0, a 40 percent chance of making $100, and a 10 percent chance of losing $100. Calculate the expected value and variance of the payoff. How does your estimate compare to the previous exercise?

3 You have a 1 percent chance of having healthcare bills of $100,000, a 19 percent chance of having healthcare bills of $10,000, a 60 percent chance of having healthcare bills of $500, and a 20 percent chance of having healthcare bills of $0. What is your expected spending?

4 You have a 2 percent chance of having healthcare bills of $100,000, a 20 percent chance of having healthcare bills of $10,000, a 60 percent chance of having healthcare bills of $500, and an 18 percent chance of having healthcare bills of $0. What is your expected healthcare spending? How does it compare to the answer in exercise 3?

5 You have a 1 percent chance of having healthcare bills of $100,000, a 19 percent chance of having healthcare bills of $10,000, a 60 percent chance of having healthcare bills of $500, and a 20 percent chance of having healthcare bills of $0. What is your expected spending? Would you be willing to buy complete insurance coverage if it cost $3,712? Explain.

6 Instead of complete insurance as in exercise 4.5, you have a policy with a $5,000 deductible. What will your expected out-of- pocket spending be? What will your expected insurance benefits be? Assuming that the premium equals 116 percent of expected insurance benefits, do you prefer the policy with a $5,000 deductible or the policy with complete coverage? Explain.

7 Your firm, which operates a nationwide system of cancer clinics, has annual profits of $800 million and cash reserves of $500 million. Your clinics have a replacement value of $200 million, and fire insurance for them would cost $5 million per year. Actuarial data show that your expected losses due to fire are $4 million. Should you buy insurance?