A Note on Optimal Insurance in the presence of a Nonpecuniary Background Risk

This note examines the theory of optimal insurance purchasing in the presence of a nonpecuniary background risk. The occurrence of the qualitative uninsurable background loss can increase, decrease or can leave the marginal utility of wealth unchanged, whereas a financial background loss (as in Doherty and Schlesinger, 1883a) always increases it. Existing theorems on the optimal level of insurance and the optimal form of insurance contracts are shown to hold only under restrictive assumptions on the correlation level between risks. The paper shows that sufficient conditions for the validity of the theorems depend not only on the correlation between the insurable and noninsurable losses, but also on the variation of the marginal utility of wealth with respect to the nonpecuniary variable.