A SimILS-based methodology for a portfolio optimization problem with stochastic returns

Combinatorial optimization has been at the heart of financial and risk management. This body of research is dominated by the mean-variance efficient frontier (MVEF) that solves the portfolio optimization problem (POP), pioneered by Harry Markowitz. The classical version of the POP minimizes risk for a given expected return on a portfolio of assets by setting the weights of those assets. Most authors deal with the variability of returns and covariances by employing expected values. In contrast, we propose a simheuristic methodology (combining the simulated annealing metaheuristic with Monte Carlo simulation), in which returns and covariances are modeled as random variables following specific probability distributions. Our methodology assumes that the best solution for a scenario with constant expected values may have poor performance in a dynamic world. A computational experiment is carried out to illustrate our approach.