Optimal Insurance for Prudent Risk Averters and Risk Lovers

Abstract

This paper examines the structure of optimal insurance contracts for a broad class of insureds that includes both risk averters and risk lovers and by assuming that the insureds are prudent. We specify the difference in optimal contract form between risk averters and risk lovers. Treating these decision-makers as a unique group, we show that the optimal insurance form is dual limited stop-loss insurance with an upper limit, which implies that including risk lovers in the group of decision-makers changes the contract in the small loss part. We also consider the situation of contracts with a concave payoff, where the optimal contract form becomes limited change-loss insurance or limited dual change-loss insurance depending on the coefficient of variation of the retained loss. Finally, we derive the form of optimal contracts in the presence of a background risk.