Multi-stage portfolio selection problem with dynamic stochastic dominance constraints

Yu Mei (), Zhiping Chen (), Jia Liu () and Bingbing Ji ()
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Yu Mei: Xi’an Jiaotong University
Zhiping Chen: Xi’an Jiaotong University
Jia Liu: Xi’an Jiaotong University
Bingbing Ji: Xi’an Jiaotong University

Journal of Global Optimization, 2022, vol. 83, issue 3, No 10, 585-613

Abstract: 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.

Keywords: Stochastic dominance; Multi-stage portfolio selection; Stochastic optimization; Scenario tree; Linear programming; 90C15; 90C26 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-021-01113-z

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