The Two Fundamental Theorems of Asset Pricing for a Class of Continuous Time Financial Markets

Abstract

The paper is concerned with the first and the second fundamental theorems of asset pricing in the case of non-exploding financial markets, in which the excess-returns from risky securities represent continuous semimartingales with absolutely continuous predictable characteristics. For such markets, the notions of "arbitrage'' and "completeness'' are characterized as properties of the distribution law of the excess-returns. It is shown that any form of arbitrage is tantamount to guaranteed arbitrage, which leads to a somewhat stronger version of the first fundamental theorem. New proofs of the first and the second fundamental theorems, which rely exclusively on methods from stochastic analysis, are established.

Keywords: Arbitrage and completeness of financial markets, the first and the second fundamental theorems of asset pricing, Ito-processes, predictable representation of local martingales, extremal martingale measures

JEL Classification: G12