Reinsurance as a Cooperative Game

Abstract

We define axiomatically a concept of value for games without transferable utilities, without introducing the usual symmetry axiom. The model, a generalization of a previous paper extending Nash’s bargaining problem, attempts to take into account the affinities between the players, defined by an a priori set of “distances”. This new value concept in then applied to compute the value of a reinsurance model. It is shown that the exchange of risks between insurance companies can be formulated as a n-person cooperative game without transferable utilities. The determination of an “optimal reinsurance treaty” is then shown to coincide with the computation of the value of the corresponding game. A complete example is given.