Criteria for the Absence and Existence of Arbitrage in Multi-Dimensional Diffusion Markets

Abstract

In this article, we study the set of equivalent (local) martingale measures for financial markets driven by multi-dimensional diffusions. We give conditions for the existence of equivalent (local) martingale measures in terms of existence and uniqueness properties of martingale problems. Based on these we derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures. As an application, we construct a financial market in which the number of risky assets determines the absence of arbitrage and equals the number of sources of risk.