The notion of a Bowley optimum has gained recent popularity as an equilibrium concept in problems of risk sharing and optimal reinsurance. In this paper, we examine the relationship between Bowley optimality and Pareto efficiency in a problem of optimal reinsurance, under fairly general preferences. Specifically, we show that Bowley-optimal contracts are indeed Pareto efficient but they make the insurer indifferent with the status quo (hence providing a partial first welfare theorem). Moreover, we show that only those Pareto-efficient contracts that make the insurer indifferent between suffering the loss and entering into the reinsurance contract are Bowley optimal (hence providing a partial second welfare theorem). We interpret these result as indicative of the limitations of Bowley optimality as an equilibrium concept in this literature. We also discuss relationships with competitive equilibria, and we provide illustrative examples.

鲍利最优的概念最近作为风险分担和最优再保险问题的均衡概念而广受欢迎。在本文中，我们在相当普遍的偏好下研究了最优再保险问题中鲍利最优性和帕累托效率之间的关系。具体来说，我们表明鲍利最优合同确实是帕累托有效的，但它们使保险公司对现状漠不关心（因此提供了部分第一福利定理）。此外，我们表明，只有那些使保险公司在遭受损失和签订再保险合同之间无动于衷的帕累托有效合同是鲍利最优的（因此提供了部分第二福利定理）。我们将这些结果解释为表明鲍利最优性在本文献中作为平衡概念的局限性。