An Riemannian Geometry Underlying Stochastic Algorithm for the Risk-free log-Optimal Portfolio Problem

The risk-free log-optimal portfolio problem is very valuable in computational finance in practice. This paper proposes an intrinsic natural gradient-based stochastic algorithm for solving the pro-(blem). The advantage of the algorithm is that the resulting iteration vector always satisfies the constrained conditions, and it is also an interior point algorithm in essence, so has a good rate of convergence. Finally, this algorithm is applied to the real data from the Exchange Institute of Shanghai Security. The numerical results are satisfactory and the reasonable financial explanation is also suggested.