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Multi-stage portfolio selection problem with dynamic stochastic dominance constraints

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Abstract

We study the multi-stage portfolio selection problem where the utility function of an investor is ambiguous. The ambiguity is characterized by dynamic stochastic dominance constraints, which are able to capture the dynamics of the random return sequence during the investment process. We propose a multi-stage dynamic stochastic dominance constrained portfolio selection model, and use a mixed normal distribution with time-varying weights and the K-means clustering technique to generate a scenario tree for the transformation of the proposed model. Based on the scenario tree representation, we derive two linear programming approximation problems, using the sampling approach or the duality theory, which provide an upper bound approximation and a lower bound approximation for the original nonconvex problem. The upper bound is asymptotically tight with infinitely many samples. Numerical results illustrate the practicality and efficiency of the proposed new model and solution techniques.

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Authors and Affiliations

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

    Yu Mei, Zhiping Chen, Jia Liu & Bingbing Ji

  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

    Yu Mei, Zhiping Chen, Jia Liu & Bingbing Ji

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  1. Yu Mei
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  2. Zhiping Chen
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  3. Jia Liu
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  4. Bingbing Ji
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Correspondence to Zhiping Chen.

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This work was supported by the National Natural Science Foundation of China (Nos. 11991023, 11901449, 11735011)

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Mei, Y., Chen, Z., Liu, J. et al. Multi-stage portfolio selection problem with dynamic stochastic dominance constraints. J Glob Optim 83, 585–613 (2022). https://doi.org/10.1007/s10898-021-01113-z

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  • DOI: https://doi.org/10.1007/s10898-021-01113-z

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