Optimal insurance with nonseparable background risk

The theory of optimal insurance with noninsurable background risk has previously been examined under the assumption that the background risk and insurable loss random variables are additively separable within the agent's utility function. In this study, these two variables are nonseparable because marginal insurable loss is positively dependent on the outcome of the background risk variable. This positive dependence implies that background risk has a smaller marginal impact on profits at higher levels of insurable loss. The optimal contract is shown to require coinsurance above a deductible minimum when the agent is prudent. This result is opposite Gollier's (1996) finding that a "disappearing deductible" is optimal when a higher level of insurable loss implies a more risky distribution of the background risk variable. With relatively weak restrictions on the various functions, the optimal indemnity schedule is a convex function of loss and the slope of this function is inversely related to certainty income.