Martingales and the Valuation of Redundant Assets

We explore foundational issues in the theory of arbitrage. Given a probabilistic model of a fixed set of securities, an equivalent martingale measure is a probability measure equivalent to the original measure which causes the securities to earn in expectation at the riskiness rate. No arbitrage opportunities exist if there exists at least one equivalent martingale measure. A contingent claim can be valued by arbitrage if it has common expectation under all equivalent martingale measures. In a general vector diffusion model, there is a unique equivalent martingale measure, thus all contingent claims can be valued by arbitrage.