ABSTRACT Unlike sophisticated institutional insurance buyers, individual insurance seekers often use simple heuristic tools for risk management purposes, such as requiring that an insurance arrangement will not result in a retained loss that exceeds a certain predetermined and fixed level. In this paper, we re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss; but we further impose an additional upper-limit constraint on the retained loss and assume that the insurer distorts his subjective probability measure. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. We characterize the optimal retention function and show that it has a simple two-part structure: zero retention (full insurance) on an event to which the insurer assigns zero probability, and a retention that could be described as a limited variable deductible on the complement of this event. As an illustration, we examine the case of a distorted Esscher premium principle.

中文翻译：

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具有保留损失上限的预算约束最优保留

摘要 与成熟的机构保险购买者不同，个人保险寻求者通常使用简单的启发式工具进行风险管理，例如要求保险安排不会导致超过某个预定和固定水平的保留损失。在本文中，我们重新审视了当被保险人和保险人对实现可保损失的可能性存在分歧时，预算受限的保险赔偿需求问题；但我们进一步对保留损失施加了额外的上限约束，并假设保险人扭曲了他的主观概率度量。我们不会对可受理的赔偿施加无破坏条件。相反，我们强加了保险公司可以承担的状态验证成本，以验证损失的严重程度，这排除了因被保险人可能误报损失而导致的事后道德风险问题。我们描述了最佳留存函数，并表明它具有简单的两部分结构：保险人为其分配零概率的事件的零留存（全额保险），以及可被描述为补充上可扣除的有限变量的留存本次活动。作为例证，我们考察了扭曲的埃舍尔溢价原则的案例。以及可被描述为此事件补充的有限可变免赔额的保留。作为例证，我们考察了扭曲的埃舍尔溢价原则的案例。以及可被描述为此事件补充的有限可变免赔额的保留。作为例证，我们考察了扭曲的埃舍尔溢价原则的案例。