Multi-period mean-variance portfolio optimization based on Monte-Carlo simulation

We propose a simulation-based approach for solving the constrained dynamic mean-variance portfolio management problem. For this dynamic optimization problem, we first consider a sub-optimal strategy, called the multi-stage strategy, which can be utilized in a forward fashion. Then, based on this fast yet sub-optimal strategy, we propose a backward recursive programming approach to improve it. We design the backward recursion algorithm such that the result is guaranteed to converge to a solution, which is at least as good as the one generated by the multi-stage strategy. In our numerical tests, highly satisfactory asset allocations are obtained for dynamic portfolio management problems with realistic constraints on the control variables.