In this paper, the optimal insurance design is studied from the perspective of an insured, who faces an insurable risk and a background risk. For the reduction of ex post moral hazard, alternative insurance contracts are asked to satisfy the principle of indemnity and the incentive-compatible condition. As in the literature, it is assumed that the insurer calculates the insurance premium solely on the basis of the expected indemnity. When the insured has a general mean-variance preference, an explicit form of optimal insurance is derived explicitly. It is found that the stochastic dependence between the background risk and the insurable risk plays a critical role in the insured’s risk transfer decision. In addition, the optimal insurance policy can often change significantly once the incentive-compatible constraint is removed.

本文从面临可保风险和背景风险的被保险人的角度研究最优保险设计。为减少事后道德风险方面，要求替代保险合同满足赔偿原则和激励兼容条件。如文献中所述，假定保险人仅根据预期赔偿额来计算保险费。当被保险人具有一般均值方差偏好时，便会明确得出最优保险的明确形式。发现本底风险与可保风险之间的随机依赖性在被保险人的风险转移决策中起着至关重要的作用。此外，一旦取消了激励兼容的约束，最优保险单往往会发生重大变化。