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Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach

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  • Wei, J.
  • Wong, K.C.
  • Yam, S.C.P.
  • Yung, S.P.

Abstract

In this article, we provide the first study in the time consistent solution of the mean–variance asset–liability management (MVALM). The framework is even considered under a continuous time Markov regime-switching setting. Using the extended Hamilton–Jacobi–Bellman equation (HJB) (see Björk and Murgoci (2010)), we show that the time consistent equilibrium control is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the similar problem in Björk and Murgoci (2010), in which it is independent of the state. Finally, we give a numerical comparison between our work with the corrected version (as obtained here) of pre-commitment strategy in Chen et al. (2008).

Suggested Citation

  • Wei, J. & Wong, K.C. & Yam, S.C.P. & Yung, S.P., 2013. "Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 281-291.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:281-291
    DOI: 10.1016/j.insmatheco.2013.05.008
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    3. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
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    6. 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.
    7. Chen, Kexin & Wong, Hoi Ying, 2019. "Time-consistent mean-variance hedging of an illiquid asset with a cointegrated liquid asset," Finance Research Letters, Elsevier, vol. 29(C), pages 184-192.
    8. Wu, Huiling & Chen, Hua, 2015. "Nash equilibrium strategy for a multi-period mean–variance portfolio selection problem with regime switching," Economic Modelling, Elsevier, vol. 46(C), pages 79-90.
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    10. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
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    12. Chi Kin Lam & Yuhong Xu & Guosheng Yin, 2016. "Dynamic portfolio selection without risk-free assets," Papers 1602.04975, arXiv.org.
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