Existence and Uniqueness of Equilibrium in a Reinsurance Syndicate

In this paper we consider a reinsurance syndicate, assuming that Pareto optimal allocations exist. Under a continuity assumption on preferences, we show that a competitive equilibrium exists and is unique. Our conditions allow for risks that are not bounded, and we show that the most standard models satisfy our set of sufficient conditions, which are thus not restrictive. Our approach is to transform the analysis from an infinite dimensional to a finite dimensional setting.

Keywords: Existence of equilibrium, uniqueness of equilibrium, Pareto optimality, reinsurance model, syndicate theory, risk tolerance, exchange economy, probability distributions, Walras’ law.