You have 1 million dollars of wealth. You build an $800,000 house at the beginning of the
Question:
You have 1 million dollars of wealth. You build an $800,000 house at the beginning of the year on the east coast of Florida. During the year there is a 2% chance that the house will be destroyed by a hurricane-related flood. However, you are able to purchase flood insurance for a premium of $2 per $100 dollars of insured house value for the year. In the event that your home is destroyed by a flood, the insurance company makes a payment equal to the insured house value. You are a risk-averse agent with the utility of end-of-year wealth given by U(W) = -W-1. Assume that the interest rate for the year is 0% and that the value of the house, if unflooded, remains unchanged at the end of the year.
(a) Let x be the amount of insurance that you purchase. In terms of x, what is wealth at the end of the period if the house is not destroyed by the flood?
(b) Let x be the amount of insurance that you purchase. In terms of x, what is wealth at the end of the period if the house is destroyed by the flood?
(c) What is the expected utility in terms of the quantities given in parts (a) and (b)?
(d) How much insurance should you purchase? You wish to maximize expected utility.
(e) What percentage of the house value did you choose to insure?
(f) Given the relationship between the premium and the insured value, is the expected profit for the insurance company positive? Is the insurance contract actuarially fair?
