Pricing issues with investment flows Applications to market models with frictions

Abstract

In this paper, we study some foundational issues in the theory of asset pricing. We consider a model where any investment opportunity is described in terms of cash flows. We do not assume that there is a numéraire, the time horizon is not supposed to be finite, the investment opportunities are not specifically related to the buying and selling of securities on a financial market. In this quite general framework, we consider different possible definitions of admissible prices for a contingent flow, mainly related to arbitrage and equilibrium considerations, and for each possible definition, we characterize the set of admissible prices. Since most market imperfections, such as short sale constraints, convex cone constraints, proportional transaction costs, no borrowing or different borrowing and lending rates, etc., can fit in the preceding model for a specific set of investment opportunities, our approach with flows provides a unified framework for the study of pricing issues in market models with frictions (including imperfections on the numéraire). We generalize existing results and we obtain them all in a unified way.