Risk Exchange I: A Unification of Some Existing Results

The paper unifies certain concepts which have arisen within the field of risk exchange. Borch’s theorem on Pareto-optimal risk exchanges is shown to be derivable from a Bowley solution when there are only two participants in the risk exchange. This theorem is then extended to an n-party risk exchange by equating this to a sequence of 2-party exchanges between the n participants. Finally, the conditions for constrained Pareto-optimal risk exchanges are derived as extreme cases of Borch’s theorem. Thus Borch’s theorem and Buhlmann and Jewell’s theorem on constrained exchanges are shown to be ultimately derivable from the Bowley solution. Key words: Risk exchange, Pareto-optimal, Bowley solution, constrained risk exchange. Reinsurance Research - Market Dynamics