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Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility

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  • Li, Danping
  • Shen, Yang
  • Zeng, Yan

Abstract

This paper considers the derivative-based optimal investment strategies for an asset–liability management (ALM) problem under the mean–variance criterion in the presence of stochastic volatility. Specifically, an asset–liability manager is allowed to invest not only in a risk-free bond and a stock, but also in a derivative, whose price depends on the underlying price of the stock and its volatility. By solving a system of two backward stochastic differential equations, we derive the explicit expressions of the efficient strategies and the corresponding efficient frontiers in two cases, with and without the derivative asset. Moreover, we consider the special case of an optimal investment problem with no liability commitment, which is also not studied in the literature. We also provide some numerical examples to illustrate our results and find that the efficient frontier of the case with the derivative is always better than that of the case without the derivative. Moreover, under the same variance, the expectation of the case with the derivative can reach up to as twice as that of the case without the derivative in some situations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:72-86
    DOI: 10.1016/j.insmatheco.2017.11.006
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    References listed on IDEAS

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    3. Xue, Xiaole & Wei, Pengyu & Weng, Chengguo, 2019. "Derivatives trading for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 40-53.
    4. Yu Yang & Yonghong Wu & Benchawan Wiwatanapataphee, 2020. "Time-consistent mean–variance asset-liability management in a regime-switching jump-diffusion market," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 401-427, December.
    5. 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.
    6. L.J. Basson & Sune Ferreira-Schenk & Zandri Dickason-Koekemoer, 2022. "Fractal Dimension Option Hedging Strategy Implementation During Turbulent Market Conditions in Developing and Developed Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 12(2), pages 84-95, March.
    7. Esfandi, Elaheh & Mousavi, Mir Hossein & Moshrefi, Rassam & Farhang-Moghaddam, Babak, 2020. "Insurer Optimal Asset Allocation in a Small and Closed Economy: The Case of Iran’s Social Security Organization," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 15(4), pages 445-461, October.
    8. Aiqin Ma & Cuiyun Zhang & Yubing Wang, 2023. "Optimal Consumption and Investment Problem under 4/2-CIR Stochastic Hybrid Model," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    9. Yan, Tingjin & Wong, Hoi Ying, 2020. "Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 105-119.
    10. Matt Davison & Marcos Escobar-Anel & Yichen Zhu, 2022. "Optimal market completion through financial derivatives with applications to volatility risk," Papers 2202.08148, arXiv.org.

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    More about this item

    Keywords

    Asset–liability management; Derivative investment; Mean–variance criterion; Stochastic volatility; Backward stochastic differential equation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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