Optimal portfolio choice with benchmarks

We construct an algorithm that makes it possible to numerically obtain an investor's optimal portfolio under general preferences. In particular, the objective function and risks constraints may be driven by benchmarks (reflecting state-dependent preferences). We apply the algorithm to various classic optimal portfolio problems for which explicit solutions are available and show that our numerical solutions are compatible with them. This observation allows us to conclude that the algorithm can be trusted as a viable way to deal with portfolio optimisation problems for which explicit solutions are not in reach.