We study the design of an optimal insurance contract in which the insured maximizes her expected utility and the insurer limits the variance of his risk exposure while maintaining the principle of indemnity and charging the premium according to the expected value principle. We derive the optimal policy semi-analytically, which is coinsurance above a deductible when the variance bound is binding. This policy automatically satisfies the incentive-compatible condition, which is crucial to rule out ex post moral hazard. We also find that the deductible is absent if and only if the contract pricing is actuarially fair. Focusing on the actuarially fair case, we carry out comparative statics on the effects of the insured's initial wealth and the variance bound on insurance demand. Our results indicate that the expected coverage is always larger for a wealthier insured, implying that the underlying insurance is a normal good, which supports certain recent empirical findings. Moreover, as the variance constraint tightens, the prudent insured cedes less losses, while the insurer is exposed to less tail risk.

我们研究了最优保险合同的设计，其中被保险人最大化其期望效用，保险公司限制其风险暴露的方差，同时维持赔偿原则并根据期望值原则收取保费。我们半分析地推导出最优保单，即当方差界限具有约束力时，共同保险高于免赔额。该政策自动满足激励相容条件，这对于排除事后道德风险至关重要。我们还发现，当且仅当合同定价在精算上公平时，免赔额才不存在。着眼于精算公平的情况，我们对被保险人的初始财富和方差界限对保险需求的影响进行了比较统计。我们的结果表明，较富裕的被保险人的预期承保范围总是较大，这意味着基础保险是正常商品，这支持了最近的某些实证研究结果。此外，随着方差约束的收紧，谨慎的被保险人放弃的损失较少，而保险公司面临的尾部风险也较小。