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Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks

Author

Listed:
  • Jian Pan

    (University of Shanghai for Science and Technology
    Gannan Normal University)

  • Qingxian Xiao

    (University of Shanghai for Science and Technology)

Abstract

This paper considers an optimal asset-liability management problem with stochastic interest rates and inflation risks under the mean–variance framework. It is assumed that there are $$n+1$$ n + 1 assets available in the financial market, including a risk-free asset, a default-free zero-coupon bond, an inflation-indexed bond and $$n-2$$ n - 2 risky assets (stocks). Moreover, the liability of the investor is assumed to follow a geometric Brownian motion process. By using the stochastic dynamic programming principle and Hamilton–Jacobi–Bellman equation approach, we derive the efficient investment strategy and efficient frontier explicitly. Finally, we provide numerical examples to illustrate the effects of model parameters on the efficient investment strategy and efficient frontier.

Suggested Citation

  • Jian Pan & Qingxian Xiao, 2017. "Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 491-519, June.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:3:d:10.1007_s00186-017-0580-6
    DOI: 10.1007/s00186-017-0580-6
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    References listed on IDEAS

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    3. 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.
    4. Jiaqi Zhu & Shenghong Li, 2020. "Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    5. Georgios I. Papayiannis, 2023. "A Framework for Treating Model Uncertainty in the Asset Liability Management Problem," Papers 2310.11987, arXiv.org.
    6. Guohui Guan, 2020. "Equilibrium and Precommitment Mean-Variance Portfolio Selection Problem with Partially Observed Price Index and Multiple Assets," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 25-47, March.
    7. Xiaoyi Zhang & Junyi Guo, 2018. "The Role of Inflation-Indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phase," Risks, MDPI, vol. 6(2), pages 1-16, March.
    8. 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.
    9. 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.
    10. Pejman Peykani & Mostafa Sargolzaei & Mohammad Hashem Botshekan & Camelia Oprean-Stan & Amir Takaloo, 2023. "Optimization of Asset and Liability Management of Banks with Minimum Possible Changes," Mathematics, MDPI, vol. 11(12), pages 1-24, June.
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    12. 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.

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