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Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon

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Abstract

This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon. Unlike previous works, the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion. The Markov chain is assumed to be independent of Brownian motion, thus the market is incomplete. The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem. The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier. All the results are different from those in the problem with fixed time horizon.

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Author information

Authors and Affiliations

  1. Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, 250100, China

    Tian Chen

  2. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    Ruyi Liu

  3. School of Mathematics, Shandong University, Jinan, 250100, China

    Zhen Wu

Authors
  1. Tian Chen
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  2. Ruyi Liu
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  3. Zhen Wu
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Corresponding author

Correspondence to Zhen Wu.

Additional information

This research was supported by the Natural Science Foundation of China under Grant Nos. 11831010, 12001319 and 61961160732, Shandong Provincial Natural Science Foundation under Grant Nos. ZR2019ZD42 and ZR2020QA025, The Taishan Scholars Climbing Program of Shandong under Grant No. TSPD20210302, Ruyi Liu acknowledges the Discovery Projects of Australian Research Council (DP200101550) and the China Postdoctoral Science Foundation (2021TQ0196).

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Chen, T., Liu, R. & Wu, Z. Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon. J Syst Sci Complex 36, 457–479 (2023). https://doi.org/10.1007/s11424-023-1272-3

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  • DOI: https://doi.org/10.1007/s11424-023-1272-3

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