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In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using non-anticipative investment strategies, in terms of the smallest positive solution to a parabolic partial differential inequality; this is determined entirely on the basis of the covariance structure of the model. The solution is also used to generate the investment strategy that realizes the best possible arbitrage. Some extensions to non-Markovian situations are also presented.
