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On mean-variance portfolio selection under a hidden Markovian regime-switching model

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  • Elliott, Robert J.
  • Siu, Tak Kuen
  • Badescu, Alex

Abstract

We study a mean-variance portfolio selection problem under a hidden Markovian regime-switching Black-Scholes-Merton economy. Under this model, the appreciation rate of a risky share is modulated by a continuous-time, finite-state hidden Markov chain whose states represent different states of an economy. We consider the general situation where an economic agent cannot observe the "true" state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes. By exploiting the separation principle, we discuss the mean-variance portfolio selection problem and the filtering-estimation problem separately. We determine an explicit solution to the mean-variance problem using the stochastic maximum principle so that we do not need the assumption of Markovian controls. We also provide robust estimates of the hidden state of the chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model. This simplifies the filtering-estimation problem.

Suggested Citation

  • Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alex, 2010. "On mean-variance portfolio selection under a hidden Markovian regime-switching model," Economic Modelling, Elsevier, vol. 27(3), pages 678-686, May.
    • Handle: RePEc:eee:ecmode:v:27:y:2010:i:3:p:678-686
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    1. Benjamín Vallejo Jiménez & Francisco Venegas Martínez, 2017. "Optimal consumption and portfolio rules when the asset price is driven by a time-inhomogeneous Markov modulated fractional Brownian motion with," Economics Bulletin, AccessEcon, vol. 37(1), pages 314-326.
    2. Eun-chong Kim & Han-wook Jeong & Nak-young Lee, 2019. "Global Asset Allocation Strategy Using a Hidden Markov Model," JRFM, MDPI, vol. 12(4), pages 1-15, November.
    3. Reza Keykhaei, 2020. "Portfolio selection in a regime switching market with a bankruptcy state and an uncertain exit-time: multi-period mean–variance formulation," Operational Research, Springer, vol. 20(3), pages 1231-1254, September.
    4. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    5. Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
    6. Zhang, Caibin & Liang, Zhibin, 2022. "Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    7. Xianggang Lu, 2019. "Block Trading: Building up a Stock Position Under a Regime Switching Model," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 805-828, September.
    8. Levy, Moshe & Kaplanski, Guy, 2015. "Portfolio selection in a two-regime world," European Journal of Operational Research, Elsevier, vol. 242(2), pages 514-524.
    9. Yao, Haixiang & Li, Zhongfei & Chen, Shumin, 2014. "Continuous-time mean–variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 36(C), pages 244-251.
    10. Shelly Singhal & Pratap Chandra Biswal, 2021. "Dynamic Commodity Portfolio Management: A Regime-switching VAR Model," Global Business Review, International Management Institute, vol. 22(2), pages 532-549, April.
    11. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    12. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Financial Science Trends and Perspectives: A Review Article," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    13. Huiling Wu, 2013. "Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 918-934, September.
    14. Hsu, Yuan-Lin & Lin, Shih-Kuei & Hung, Ming-Chin & Huang, Tzu-Hui, 2016. "Empirical analysis of stock indices under a regime-switching model with dependent jump size risks," Economic Modelling, Elsevier, vol. 54(C), pages 260-275.
    15. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Tendencias y perspectivas de la ciencia financiera: Un artículo de revisión," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    16. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2013. "Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment," Economic Modelling, Elsevier, vol. 31(C), pages 12-17.
    17. Daniela Neykova & Marcos Escobar & Rudi Zagst, 2015. "Optimal investment in multidimensional Markov-modulated affine models," Annals of Finance, Springer, vol. 11(3), pages 503-530, November.
    18. Su, Xiaoshan & Bai, Manying & Han, Yingwei, 2021. "Robust portfolio selection with regime switching and asymmetric dependence," Economic Modelling, Elsevier, vol. 99(C).
    19. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
    20. De Gooijer, Jan G. & Henter, Gustav Eje & Yuan, Ao, 2022. "Kernel-based hidden Markov conditional densities," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    21. Akhter Mohiuddin Rather & V. N. Sastry & Arun Agarwal, 2017. "Stock market prediction and Portfolio selection models: a survey," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 558-579, September.
    22. Yao, Haixiang & Zeng, Yan & Chen, Shumin, 2013. "Multi-period mean–variance asset–liability management with uncontrolled cash flow and uncertain time-horizon," Economic Modelling, Elsevier, vol. 30(C), pages 492-500.
    23. Reetam Majumder & Qing Ji & Nagaraj K. Neerchal, 2023. "Optimal Stock Portfolio Selection with a Multivariate Hidden Markov Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 177-198, May.
    24. Y. Zhang & Z. Jin & J. Wei & G. Yin, 2022. "Mean-variance portfolio selection with dynamic attention behavior in a hidden Markov model," Papers 2205.08743, arXiv.org.

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