Bowley vs. Pareto optima in reinsurance contracting

Abstract

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.