Mean-VaR portfolio optimization: A nonparametric approach

Portfolio optimization involves the optimal assignment of limited capital to different available financial assets to achieve a reasonable trade-off between profit and risk. We consider an alternative Markowitz’s mean–variance model in which the variance is replaced with an industry standard risk measure, Value-at-Risk (VaR), in order to better assess market risk exposure associated with financial and commodity asset price fluctuations. Realistic portfolio optimization in the mean-VaR framework is a challenging problem since it leads to a non-convex NP-hard problem which is computationally intractable. In this work, an efficient learning-guided hybrid multi-objective evolutionary algorithm (MODE-GL) is proposed to solve mean-VaR portfolio optimization problems with real-world constraints such as cardinality, quantity, pre-assignment, round-lot and class constraints. A learning-guided solution generation strategy is incorporated into the multi-objective optimization process to promote efficient convergence by guiding the evolutionary search towards promising regions of the search space. The proposed algorithm is compared with the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2). Experimental results using historical daily financial market data from S & P 100 and S & P 500 indices are presented. The results show that MODE-GL outperforms two existing techniques for this important class of portfolio investment problems in terms of solution quality and computational time. The results highlight that the proposed algorithm is able to solve the complex portfolio optimization without simplifications while obtaining good solutions in reasonable time and has significant potential for use in practice

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines