Dear Forum,currently I am struggling with a multi-period portfolio optimization problem subject to constraints on the portfolio weights. I am trying to evaluate the expected utility of a specific portfolio by running a Monte-Carlo simulation. If you look at a small number of assets you can discretize the control space (portfolio weights) and compute the expected utility of all possible asset combinations. The portfolio with the highest simulated expected utility is of course the optimal portfolio. But what happens when you have many assets? The described method is subject to the curse of dimensionality and computation time explodes. Now, here is my question: is there a way to numerically search for the optimal portfolio without having to evaluate all admissible portfolios? It should be a method that does not rely on gradients, since the function I am trying to maximize is a conditional expectation, and its explicit form is unknown...Thanks a lot,Costica.

Albeit you dont provide a clear picture of your problem settings you can find out some some answers in Zenios' papers and the references there in.RegardsAnthis

If you don't want to use the gradient you might have to rely on a direct search method, e.g. Nelder-Mead (Simplex search) or Hooke and Jeeves. I have succesfully used Nelder-Mead for solving minimization problems (in a completely different context). However, the method does tend to become inefficient for large-dimensional problems. One useful reference is J.C. Nash "Compact Numerical Methods for Computers".Regards,Niclas

From the hazy picture I get of your prolem it seems to me that you will have a large number of local maxima, further the constraints will tend to make localmaxima next to forbidden allocation.My (high level) algortihm would be to 1: cast a set of random numbers that obey your constraints.2: Perturb each of your allocations by a random small amount within constraints3: Whichever single change causes the greatest movement improvement, apply.4: If there is a "worthwhile" change, goto 2:5: If portfolio "good enough" stop6: goto 1:The peturbations should be of the form X->X*Perturb, since of course adding as a pertrurbation will take a long time to get you anywhere.# I have some code I could illustrate this with if you're interested.

Thank you all for the helpful suggestions.Dominic, I am very interested in seeing your code. I will write you a private message with my e-mail address.Best,costica.

I have some experience in computing conditonal expectations via Malliavin calculus. It would be helpful you could be more specific about the setting, or if you could send it to me via my e-mail: greenleaves01@gmail.com

You may wish to try genetic algorithms or evolution strategies. In particular CMA-ES, the covariance matrix adaptation evolution strategy can be quite fast and does not use gradients.