Trading in Markovian Price Models

We examine a Markovian model for the price evolution of a stock, in which the probability of local upward or downward movement is arbitrarily dependent on the current price itself (and perhaps some auxiliary state information). This model directly and considerably generalizes many of the most well-studied price evolution models in classical nance, including a variety of random walk, drift and di usion models. Our main result is a \universally pro table" trading strategy | a single xed strategy whose pro tability competes with the optimal strategy (which knows all of the underlying parameters of the in nite and possibly nonstationary Markov process).