Abstract We analyze the optimal coverage level for an unreliable insurance contract when 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 driven 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 risk in insurance contracts.

中文翻译：

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有时更多，有时更少：谨慎和风险保险范围的多样化

摘要 我们分析了当效用最大化的投保人可以将内在的不履约风险转移给几个共同保险公司时，不可靠的保险合同的最佳承保水平。我们的讨论从违约风险下的保险需求模型和引入称为共同保险政策的多重风险分担工具开始。随后，我们研究了回收率与最佳覆盖水平、投保人的效用以及限额内的最佳覆盖水平之间的相互关系。然后，我们考虑了共同保险公司数量不断变化和违约相关性增加的最佳覆盖水平的单调性。我们建议的标准表明，保单持有人对更多或更少保险的偏好主要取决于他们的审慎程度。