Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2024, Vol. 41 ›› Issue (2): 232-244.doi: 10.3969/j.issn.1005-3085.2024.02.003

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Multi-stage Bayesian Reinforcement Learning Robust Portfolio Selection Model

LI Roujia,  DUAN Qihong,  FENG Zhuohang,  LIU Jia   

  1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2021-04-30 Accepted:2021-08-27 Online:2024-04-15 Published:2024-06-15
  • Contact: J. Liu. E-mail address: jialiu@xjtu.edu.cn
  • Supported by:
    The National Key R&D Program of China (2022YFA1004000); the National Natural Science Foundation of China (11991023; 12371324).

Abstract:

The estimation of uncertainty sets in traditional multi-stage distributionally robust portfolio selection models is a challenging problem. This paper applys the Bayesian reinforcement learning technique to dynamically update the first two order moments in the uncertainty sets of a multi-stage distributionally robust model. We study the mean-worst case robust CVaR model in the Bayesian reinforcement learning framework. We propose a two-level decomposition solution framework by combining dynamic programming techniques and the progressive hedging algorithm. The lower level finds optimal policies of sub-models with given model parameters by solving a series of second-order cone programming problems. While the upper level finds an implementable policy satisfying non-anticipation constraints by using Bayes'~law. Numerical results in the US stock market illustrate the superior out-of-sample investment performance of the multi-stage Bayesian reinforcement learning robust portfolio selection model.

Key words: Bayesian reinforcement learning, robust risk measure, portfolio selection, second-order cone programming