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On Viable Diffusion Price Processes of the Market Portfolio

Authors

  • AVI BICK

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    • Faculty of Commerce and Business Administration, The University of British Columbia. A previous version of this paper titled “Identifying the Utility Function Corresponding to a Given Stock Price Process” was presented at the Western Finance Association meetings (1986). With the usual caveat, I thank Darrel Duffie, David Feldman, Farshid Jamashidian, Andrew Lo, Bernt Øksendal, Haim Reisman, and participants in seminars at NYU, the Hebrew University of Jerusalem, Haifa University, Tel Aviv University, Carnegie-Mellon University, the Wharton School, the University of Houston, and UBC for their helpful comments. Valuable suggestions by an anonymous referee and by the editor, René Stulz, have helped to improve the paper.

ABSTRACT

The assumption that the market portfolio follows a specified diffusion process implies, in a simple equilibrium framework, that the representative individual must have a certain utility function which is identified in the paper. Not every diffusion process is viable, i.e., can be “endogenized” to be the market portfolio's price process in such an equilibrium model. The paper provides necessary and sufficient conditions for viability which imply that viable diffusion processes constitute a rather restricted family.

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