Sometimes more, sometimes less: Prudence and the diversification of risky insurance coverage

Abstract

We analyze the optimal coverage level for an unreliable insurance contract if a utility-maximizing policyholder can transfer the intrinsic nonperformance risk to several co-insurers. Our discussion starts with an insurance demand model under default risk and the introduction of a multiple risk-sharing instrument called co-insurance policy. Subsequently, we examine the interrelation between the recovery rate and the optimal coverage level, the utility of the policyholder, and the optimal coverage level in the limit. We then consider the monotonicity of the optimal coverage level for a changing number of co-insurers and an increasing default correlation. Our proposed criteria indicate that the policyholders’ preferences for more or less coverage are primarily determined by their degree of prudence. We conclude that more prudent policyholders are more likely to accept the costs for any risk management measure intended to provide a hedge against default rik in insurance contracts.