Séminaire du CIMMUL – Mario Ghossoub

Bowley vs. Pareto Optima in Reinsurance Contracting

Mario Ghossoub

Professeur
Statistics and Actuarial Science, University of Waterloo

Résumé

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, while we show that Bowley-optimal contracts are indeed Pareto efficient (hence providing a first welfare theorem), we also 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 only a partial second welfare theorem). We interpret the latter 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 an illustrative example.