The Nash Bargaining Solution vs. Equilibrium in a Reinsurance Syndicate
25 Pages Posted: 16 Jun 2008
Date Written: May 30, 2008
We compare the Nash bargaining solution in a reinsurance syndicate to the competitive equilibrium allocation, focusing on uncertainty and risk aversion. Restricting attention to proportional reinsurance treaties, we find that, although these solution concepts are very different, one may just appear as a first order Taylor series approximation of the other, in certain cases. This may be good news for the Nash solution, or for the equilibrium allocation, all depending upon one's point of view.
Our model also allows us to readily identify some properties of the equilibrium allocation not be shared by the bargaining solution, and vice versa, related to both risk aversions and correlations.
Keywords: Nash's Bargaining Solution, Equilibrium, Pareto Optimal Risk Exchange, Reinsurance Treaties, Uncertainty, Risk Aversion, Correlations, Multinormal Universe
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