Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing

In this paper, we give a uni ed approach to equilibrium asset pricing theories. We de ne a factor subspace and develop a general equilibrium model with an in nite dimensional contingent claim space which will be applied to asset pricing models. We show that there exists a minimal factor subspace F in the sense that no proper subspace of F can serve a factor subspace. We discuss how the minimal F can be determined endogenously given a market structure. The analysis in this paper can be applied to: Economy without aggergate risk; CAPM with elliptical distributions; Equilibrium version of APT; Economy with call options. * I would like to thank A. Mclennan, S. LeRoy, and E. Green for their helpful comments and suggestions. I would especially like to thank J.Werner for his encouragement and guidance. Commments from seminar participants at Mathematical Economics Workshop, University of Minnesota, are greatly acknowledged. Of course, all remaining errors are mine.