Valuation of Risky Assets in Arbitrage Free Economies with Frictions



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    • Arizona State University. The author acknowledges Stephen Ross, the participants of the ORSA/TIMS meeting (November 1985) for helpful comments, and Jaime Dermody for helping improve the exposition of the paper. This paper was inspired from a paper by Garman and Ohlson [2], in particular from the footnote, “A treatment of the relaxed assumption (linearity of transaction costs) would lead into nonlinear duality theory …”. The research was supported in part by the Council 100 grant from Arizona State University.


This paper derives a framework for arbitrage models in markets with frictions. It generalizes the existence of a valuation operator to such markets. As in perfect markets, the valuation operator is a linear operator and its existence is implied by the no-arbitrage condition. In imperfect markets the valuation operator is individual-specific and depends on the agent's position in the market. The methodology employed in the paper is duality in convex programming.