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A sparse chance constrained portfolio selection model with multiple constraints

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Abstract

This paper presents a general sparse portfolio selection model with expectation, chance and cardinality constraints. For the sparse portfolio selection model, we derive respectively the sample based reformulation and distributionally robust reformulation with mixture distribution based ambiguity set. These reformulations are mixed-integer programming problem and programming problem with difference of convex functions (DC), respectively. As an application of the general model and its reformulations, we consider the sparse enhanced indexation problem with multiple constraints. Empirical tests are conducted on the real data sets from major international stock markets. The results demonstrate that the proposed model, the reformulations and the solution method can efficiently solve the enhanced indexation problem and our approach can generally achieve sparse tracking portfolios with good out-of-sample excess returns and high robustness.

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Acknowledgements

The authors express their heart-felt thanks to the handling editors and two anonymous reviewers for their insightful, constructive and detailed comments and suggestions, which have helped us to substantially improve the presentation and quality of this manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Zhiping Chen & Shen Peng

  2. Center for Optimization Technique and Quantitative Finance, Xi’an International Academy for Mathematics and Mathematical Technology, Xi’an, 710049, Shaanxi, People’s Republic of China

    Zhiping Chen & Shen Peng

  3. Laboratoire de Recherche en Informatique, Université Paris Sud, 91405, Orsay, France

    Shen Peng & Abdel Lisser

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  1. Zhiping Chen
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  2. Shen Peng
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Correspondence to Zhiping Chen.

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This research was supported by the National Natural Science Foundation of China (Grant Numbers 11991023, 11991020 and 11735011).

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Chen, Z., Peng, S. & Lisser, A. A sparse chance constrained portfolio selection model with multiple constraints. J Glob Optim 77, 825–852 (2020). https://doi.org/10.1007/s10898-020-00901-3

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