Viability and Equilibrium in Securities Markets with Frictions

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom suplly equals demand. This is equivalent to the existence of a positive linear pricing rule on the entire space of contingent claims an underlying frictionless linear pricing rule that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches a generalization of opportunities of arbitrage. When a market for a non marketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask We have strongly bene tted from conversations with Kerry Back, Jean-Marc Bonnisseau, George Constantinides, Darell Du e, Philip Dybvig, Ivar Ekeland, Lars Hansen, Chi-Fu Huang, Fulvio Ortu, Manuel Santos, David Schmeidler, MikeWoodford, and especially Jos e Scheinkman. We are also grateful to seminar participants at the University of Chicago for helpful comments. The nancial supports of NSF grant # SES 9022643, the Santa Fe Institute, and of the Sloan Foundation are gratefully acknowledged. This research was developed while Kallal was a liated with the University of Chicago and New York University. Salomon is not responsible for any statement or conclusions herein, and no opinions, theories, or techniques presented herein in any way represent the position of Salomon Brothers Inc. CREST-ENSAE, 15 Boulevard Gabriel Peri, 92 245 Malako Cedex, FRANCE. Salomon Brothers, 7 World Trade Center, New York, 10048, NY, USA. price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule the supremum of the underlying frictionless linear pricing rules for which the original equilibrium does not collapse, when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing