The purpose of this paper is to introduce an approximation of the kernel-based log-optimal investment strategy that guarantees an almost optimal rate of growth of the capital under minimal assumptions on the behavior of the market. The new strategy uses much less knowledge on the distribution of the market process. It is analyzed both theoretically and empirically. The theoretical results show that the asymptotic rate of growth well approximates the optimal one that one could achieve with a full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The empirical results show that the proposed semi-log-optimal and the log-optimal strategies have essentially the same performance measured on past NYSE data.
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