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Equilibrium in a Reinsurance Market

Karl Borch

Abstract

This paper investigates the possibility of generalizing the classical theory of commodity markets to include uncertainty. It is shown that if uncertainty is considered as a commodity, it is possible to define a meaningful price concept, and to determine a price which makes supply equal to demand. However, if each participant seeks to maximize his utility, taking this price as given, the market will not in general reach a Pareto optimal state. If the market shall reach a Pareto optimal state, there must be negotiations between the participants, and it seems that the problem can best be analysed as an n-person cooperative game. The paper is written in the terminology of reinsurance markets. The theoretical model studied should be applicable also to stock exchanges and other markets where the participants seek to reach an optimal distribution of risk.