A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems

He, Fang; Qu, Rong

Abstract

In this paper, we investigate a multi-period portfolio selection problem with a comprehensive set of real-world trading constraints as well as market random uncertainty in terms of asset prices. We formulate the problem into a two-stage stochastic mixed-integer program (SMIP) with recourse. The set of constraints is modelled as mixed-integer program, while a set of decision variables to rebalance the portfolio in multiple periods is explicitly introduced as the recourse variables in the second stage of stochastic program. Although the combination of stochastic program and mixed-integer program leads to computational challenges in finding solutions to the problem, the proposed SMIP model provides an insightful and flexible description of the problem. The model also enables the investors to make decisions subject to real-world trading constraints and market uncertainty.

To deal with the computational difficulty of the proposed model, a simplification and hybrid solution method is applied in the paper. The simplification method aims to eliminate the difficult constraints in the model, resulting into easier sub-problems compared to the original one. The hybrid method is developed to integrate local search with Branch-and-Bound (B&B) to solve the problem heuristically. We present computational results of the hybrid approach to analyse the performance of the proposed method. The results illustrate that the hybrid method can generate good solutions in a reasonable amount of computational time. We also compare the obtained portfolio values against an index value to illustrate the performance and strengths of the proposed SMIP model. Implications of the model and future work are also discussed.

Citation

He, F., & Qu, R. (2014). A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems. Information Sciences, 289, https://doi.org/10.1016/j.ins.2014.08.028

• Journal Article Type: Article
• Acceptance Date: Aug 8, 2014
• Online Publication Date: Aug 20, 2014
• Publication Date: Dec 24, 2014
• Deposit Date: Mar 15, 2015
• Publicly Available Date: Mar 15, 2015
• Journal: Information Sciences
• Print ISSN: 0020-0255
• Electronic ISSN: 1872-6291
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 289
• DOI: https://doi.org/10.1016/j.ins.2014.08.028
• Keywords: Stochastic programming; Hybrid algorithm; Branch-and-Bound; Local search; Portfolio selection problems
• Public URL: https://nottingham-repository.worktribe.com/output/740511
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0020025514008251
• Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Information Sciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information Sciences, 289 (2014), doi: 10.1016/j.ins.2014.08.028
• Contract Date: Mar 15, 2015