Posted: March 1st, 2017

# Will the homeowner retrofit the house, and which insurance policy will the homeowner buy? Will the insurance company make a profit (on average) given the homeowner s choice?

Suppose the typical Florida resident has wealth of \$500,000, of which his or her home is worth \$100,000. Unfortunately, Florida is in hurricane alley, and it is believed there is a 10 percent chance of a hurricae that could totally destroy the house (I.S., a loss of \$100,000). However, it is possible to retrofit the house with various protective devices (shutters, roof bolts, etc.) for a cost of \$2,000. This reduces the size of loss from a 10 percent cvhance of loss of \$100,000 to a 5 percent chance of a loss of \$50,000. The homeowner must decide whether to retrofit and thereby reduce the expected loss. The problem for an insurance company is that it does not know whether the retrofit will be chosen and therefore cannot quote a premium conditioned on the policyholder choosing this action. Nevertheless, the insurance company offers the following two policies from which the homeowner can choose: (1) The premium for insurance covering total loss is \$12,000 or (2) the premium for insurance covering only 50 percent of loss is \$1,500. The typical homeowner has a utility function equal to the square root of wealth. Will the homeowner retrofit the house, and which insurance policy will the homeowner buy? Will the insurance company make a profit (on average) given the homeowner s choice?

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