In this paper, we consider an optimal insurance problem from the perspective of a risk-averse individual who faces an insurable risk as well as some background risk and wants to maximise the expected utility of his/her final wealth. To reduce ex post moral hazard, we follow Huberman et al. (Bell J. Econ. 14:415–426 1983) to assume that alternative insurance contracts satisfy the principle of indemnity and the no-sabotage condition. When the insurance premium is calculated by the expected value premium principle, a necessary and sufficient condition for the optimality of an insurance contract is established under a general dependence structure between insurable and background risks. By virtue of this condition, some qualitative properties of optimal contracts are developed, a scheme is provided to improve any suboptimal insurance strategy, and optimal insurance forms are derived explicitly for some dependence structures of interest. These forms are not always piecewise linear.

在本文中，我们从一个规避风险的人的角度考虑一个最优保险问题，他既要面对可保风险又要承担一些背景风险，并希望最大化其最终财富的预期效用。为了减少事后道德风险，我们遵循Huberman等人的观点。（Bell J. Econ。14：415–426 1983）假设替代保险合同满足赔偿原则和无破坏性条件。当根据期望值溢价原理计算保险费时，在可保风险与背景风险之间的一般依存关系下，为保险合同的最优性建立了充要条件。在这种情况下，开发了最优合同的一些定性属性，提供了一种改进任何次优保险策略的方案，最优保险形式是针对某些利益依存关系结构明确得出的。这些形式并不总是分段线性的。