Portfolio selection with GARCH volatility dynamics

This paper proposes and compares portfolio selection models under the assumption that the portfolios of returns follow a GARCH type process. We compute the price/return distribution at some future time approximating the GARCH process with a Markov chain. We consider either a GARCH(1,1) model or an asymmetric GARCH type model (E-GARCH, GJR-GARCH) . We present an expost comparison of portfolio selection strategies applied to some assets of the US Market. Since the optimization problems present more local optima, we implement an heuristic algorithm for the global optimum in order to overcome the intrinsic computational complexity of the models.