An Adaptive Algorithm for log-optimal Portfolio and its Theoretical Analysis

In this paper, an effectively adaptive algorithm for solving log-optimal portfolio problem is proposed. It is a variant type of stochastic approximation algorithm. Since the problem considered here is a constrained optimization problem, the gradient ascent direction used conventionally is replaced by the steepest ascent tangent vector on the corresponding constraint manifold. Under some reasonable conditions, the convergence property of this algorithm is also demonstrated. Finally, this algorithm is applied to search optimal portfolio with real data of the Exchange Institute of Shanghai Security, the obtained numerical results are satisfactory.