Equivalent Martingale Measures and No-Arbitrage in Stochastic Securities Market Models

We characterize those vector-valued stochastic processes (with a finite index set and defined on an arbitrary stochastic base) which can become a martingale under an equivalent change of measure. This solves a problem which arises in the study of finite period securities markets with one riskless bond and a finite number of risky stocks. In this setting, our characterization provides necessary and sufficient conditions for the absence of arbitrage opportunities ("free lunches"). This result can be interpreted as saying "if one cannot win betting on a process, then it must be a martingale under an equivalent measure", and provides a converse to the intuitive notion that "one cannot win betting on a martingale".