This paper examines the theory of optimal insurance purchasing in the presence of uninsurable background risk. Existing theorems concerning the optimal level of insurance and the optimal form of an insurance contract are shown to hold only under restricted market and risk assumptions. In particular, conditions sufficient for the optimality of full coverage or sufficient for the optimality of deductible policies depend on the correlation between insurable and uninsurable risks. These results may provide a partial explanation why existing theory is often contradicted by observable behavior.

This paper examines the theory of optimal insurance purchasing in the presence of uninsurable background risk. Existing theorems concerning the optimal level of insurance and the optimal form of an insurance contract are shown to hold only under restricted market and risk assumptions. In particular, conditions sufficient for the optimality of full coverage or sufficient for the optimality of deductible policies depend on the correlation between insurable and uninsurable risks. These results may provide a partial explanation why existing theory is often contradicted by observable behavior.