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Portfolio optimization is one of the most important problems in the finance field. The traditional mean-variance model has its drawbacks since it fails to take the market uncertainty into account. In this work, we investigate a two-stage stochastic portfolio optimization model with a comprehensive set of real world trading constraints in order to capture the market uncertainties in terms of future asset prices. Scenarios are generated to capture uncertain prices of assets. Stability tests are performed and the results confirm the effectiveness of the scenario generation method used for this work. We propose a hybrid combinatorial approach, which integrates a hybrid algorithm and a linear programming (LP) solver for the problem with a large number of scenarios, where the hybrid algorithm is used to search for the assets selection heuristically and the LP solver solves the corresponding sub-problems of weight allocation optimally. The hybrid algorithm is based on Population Based Incremental Learning (PBIL) while local search, hash search, elitist selection, partially guided mutation and learning inheritance are also adopted. Comparison results against other 3 algorithms are given. The results show that our hybrid combinatorial approach can solve the two-stage stochastic model effectively and efficiently. The effects of different parameter settings are also examined.

Portfolio optimization is an important problem based on the modern portfolio theory (MPT) in the finance field. The idea is to maximize the portfolio expected return as well as minimizing portfolio risk at the same time. In this work, we propose a combinatorial algorithm for the portfolio optimization problem with the cardinality and bounding constraints. The proposed algorithm hybridizes a metaheuristic approach (particle swarm optimization, PSO) and a mathematical programming method where PSO is used to deal with the cardinality constraints and the math programming method is used to deal with the rest of the model. Computational results are given for the benchmark datasets from the OR-library and they indicate that it is a useful strategy for this problem. We also present the solutions obtained by the CPLEX mixed integer program solver for these instances and they can be used as the criteria for the comparison of algorithms for the same problem in the future.