### Anticipatory Stochastic Multi-objective Optimization for Uncertainty Handling in Portfolio Selection

Abstract

An anticipatory stochastic multi-objective model based on S-Metric maximization is proposed. The environment is assumed to be noisy and time-varying. This raises the question of how to incorporate anticipation in metaheuristics such that the Pareto optimal solutions can reflect the uncertainty about the subsequent environments. A principled anticipatory learning method for tracking the dynamics of the objective vectors is then proposed so that the estimated S-Metric contributions of each solution can integrate the underlying stochastic uncertainty. The proposal is assessed for minimum holding, cardinality constrained portfolio selection, using real-world stock data. Preliminary results suggest that, by taking into account the underlying uncertainty in the predictive knowledge provided by a Kalman filter, we were able to reduce the sum of squared errors prediction of the portfolios ex-post return and risk estimation in out-of-sample investment environments.