Monte Carlo Expected Wealth and Risk Measure Trade-Off Portfolio Optimization

A multiperiod portfolio optimization is described with Monte Carlo sampled risky asset paths under realistic constraints on the investment policies. The proposed approach can be used with various asset and risk models. It is flexible as it does not require dynamic programming or any transformations. As examples, the variance and semivariance risks are considered leading to mean-variance and mean-semivariance formulations, respectively. A quasi-Newton method with an adjoint gradient computation can solve the resulting optimization problems efficiently. Numerical examples show efficient frontiers together with optimal asset allocations computed for mean-variance and mean-semivariance portfolios with two and five assets.