According to K. J. Arrow, if an insurance company is willing to offer any insurance policy against loss desired by the buyer at a premium depending only on the policy's actuarial value, the policy chosen by a risk-averting buyer will take the form of 100-percent coverage above a deductible. The author shows here that if the true distribution of losses is known in advance, or if there are many identical individuals covered by the insurance and the accounts can be settled at the end of the year, the optimal insurance scheme does not have a premium. Instead, the optimal contract makes payments in as well as payments out contingent on the losses of the buyer during the year. Although information costs and moral hazard often make such contracts infeasible, examples are given in which information on the fortunate is easy to obtain and contingent contracts are useful. 7 pp. Ref. (ETG)
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