An algorithm for maximizing expected log investment return

Let the random (stock market) vector be drawn according to a known distribution function . A log-optimal portfolio is any portfolio achieving maximal expected return , where the supremum is over the simplex . An algorithm is presented for finding . The algorithm consists of replacing the portfolio by the expected portfolio , corresponding to the expected proportion of holdings in each stock after one market period. The improvement in after each iteration is lower-bounded by the Kullback-Leibler information number between the current and updated portfolios. Thus the algorithm monotonically improves the return . An upper bound on is given in terms of the current portfolio and the gradient, and the convergence of the algorithm is established.