Background risk and the performance of insurance markets under adverse selection

Background risk can influence the performance of insurance markets that must deal with adverse selection when applicants are risk vulnerable, since they are more averse to bearing the insurable risk as a result of their exposures to background risk. We show that background risk always results in a lower deductible for the incentive constrained contract, and that a broader range of markets attains the stable sequential equilibrium cross-subsidized pair of separating contracts. We conclude that background risk always improves the performance of markets for coverage against (insurable) foreground risks that must deal with adverse selection. We also find, however, that these improvements are never sufficient to offset the cost to insureds of bearing the background risk.