Abstract
P. Algoet and T. Cover characterized log-optimal portfolios in a stationary market without friction. There is no analogous result for markets with friction, of which a currency market is a typical example. In this paper we restrict ourselves to simple static strategies. The problem is then reduced to the analysis of products of random matrices, the top-Lyapunov exponent giving the growth rate. New insights to products of random matrices will be given and an algorithm for optimizing top-Lyapunov exponents will be presented together with some key steps of its analysis. Simulation results will also be given. ..
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