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Time-consistent mean–variance asset–liability management with random coefficients

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  • Wei, Jiaqin
  • Wang, Tianxiao

Abstract

In this paper, we aim to find a time-consistent open-loop equilibrium strategy for the asset–liability management problem under mean–variance criterion. The financial market consists of a bank account and m stocks whose prices are modeled by geometric Brownian motions. The liability of the investor is uncontrollable and modeled by another geometric Brownian motion which is correlated to the stock prices. First, we provide a sufficient condition for the equilibrium strategy, which involves a system of FBSDEs. Second, by solving these FBSDEs, we obtain an equilibrium strategy in a linear feedback form of the surplus and the liability. Finally, we consider a Markovian case where the interest rate is given by the Vasiček model.

Suggested Citation

  • Wei, Jiaqin & Wang, Tianxiao, 2017. "Time-consistent mean–variance asset–liability management with random coefficients," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 84-96.
    • Handle: RePEc:eee:insuma:v:77:y:2017:i:c:p:84-96
    DOI: 10.1016/j.insmatheco.2017.08.011
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    References listed on IDEAS

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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.
    4. Wang, Hao & Wang, Rongming & Wei, Jiaqin, 2019. "Time-consistent investment-proportional reinsurance strategy with random coefficients for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 104-114.
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    6. Feghhi Kashani , Mohammad & Mohebimajd , Ahmadreza, 2021. "Outperformance Testing of a Dynamic Assets Portfolio Selection Supplemented with a Continuous Paths Levy Process," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 16(2), pages 253-282, June.
    7. Yumo Zhang, 2023. "Robust Optimal Investment Strategies for Mean-Variance Asset-Liability Management Under 4/2 Stochastic Volatility Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-32, March.
    8. Ying Hu & Xiaomin Shi & Zuo Quan Xu, 2022. "Non-homogeneous stochastic LQ control with regime switching and random coefficients," Papers 2201.01433, arXiv.org, revised Jul 2023.
    9. Hanwen Zhang & Duy-Minh Dang, 2023. "A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models," Papers 2309.05977, arXiv.org.
    10. Li, Danping & Shen, Yang & Zeng, Yan, 2018. "Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 72-86.
    11. Yumo Zhang, 2022. "Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate," Annals of Finance, Springer, vol. 18(4), pages 511-544, December.
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