Existence of Consistent Price Systems

Abstract

This chapter is concerned with the existence of consistent price systems on the space of contingent claims within the framework of a partial equilibrium model. A two-date economy with uncertainty is considered in Section 3.1, and the decision problem of an agent concerning his present consumption and state contingent future consumption by means of a trading strategy in securities is stated. Section 3.2 introduces the basic “no-arbitrage” assumption and gives necessary and sufficient conditions for the existence of a price system on the space of contingent claims that is consistent with the price process of the given securities. A consistent price system can be described by means of an equivalent martingale measure. This section closely follows the reasoning of HARRISON/ KREPS (1979). Section 3.3 gives models that possess at least one equivalent martingale measure.