Optimum Insurance of Approximate Losses
J. OF RISK AND INSURANCE, Vol. 63 No. 3, September 1996
Posted: 24 Oct 1996
This article considers the problem of the optimal form of insurance contract when the indemnity can be made contingent only upon an imperfect signal of the final wealth of the insured person. This is the case, for example, when some risks affecting wealth cannot be insured by the market. The optimal contract is shown to contain a straight deductible when the distribution of the uninsurable risk is independent of the size of the loss of the insurable asset. Under a plausible condition on the utility function, the existence of an uninsurable risk reduces the optimal deductible. If the risk on the uninsurable asset increases with the size of the loss of the insurable asset, the optimal contract contains a "disappearing deductible" if the policyholder is prudent (u''' > 0). This model also is useful for analyzing the design of optimal insurance when losses are observed by the insurer with an error.
JEL Classification: D8, G22
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