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Continuous-time mean–variance asset–liability management with endogenous liabilities

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  • Yao, Haixiang
  • Lai, Yongzeng
  • Li, Yong

Abstract

This paper investigates a continuous-time mean–variance asset–liability management problem with endogenous liabilities in a more general market where all the assets can be risky. Different from exogenous liabilities that cannot be controlled, the endogenous liabilities can be controlled by various financial instruments and investors’ decisions. For example, a company can raise fund by issuing different kinds of bonds. Types and quantities of the bonds are controlled by the company itself. Investors optimize allocation not only for their assets, but also for their liabilities under our model. This makes the analysis of the problem more challenging than in the setting based on exogenous liabilities. In this paper, we first prove the existence and uniqueness of the solution to the associated Riccati-type equation by using the Khatri–Rao product technique and the relevant stochastic control theory; we then derive closed form expressions of the efficient strategy and the mean–variance efficient frontier by using the Lagrange multiplier method and the Hamilton–Jacobi–Bellman equation approach, and we next discuss two degenerated cases; finally, we present some numerical examples to illustrate the results obtained in this paper.

Suggested Citation

  • Yao, Haixiang & Lai, Yongzeng & Li, Yong, 2013. "Continuous-time mean–variance asset–liability management with endogenous liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 6-17.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:1:p:6-17
    DOI: 10.1016/j.insmatheco.2012.10.001
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    Cited by:

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    2. Zhang, Miao & Chen, Ping, 2016. "Mean–variance asset–liability management under constant elasticity of variance process," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 11-18.
    3. Chang Hao & Wang Chunfeng & Fang Zhenming, 2017. "Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework," Journal of Systems Science and Information, De Gruyter, vol. 5(3), pages 229-249, June.
    4. Duarte, Thiago B. & Valladão, Davi M. & Veiga, Álvaro, 2017. "Asset liability management for open pension schemes using multistage stochastic programming under Solvency-II-based regulatory constraints," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 177-188.
    5. Yao, Haixiang & Lai, Yongzeng & Ma, Qinghua & Jian, Minjie, 2014. "Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 84-92.
    6. 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.
    7. Jun Yu, 2014. "Optimal Asset-Liability Management for an Insurer Under Markov Regime Switching Jump-Diffusion Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 317-330, November.
    8. Chang, Hao, 2015. "Dynamic mean–variance portfolio selection with liability and stochastic interest rate," Economic Modelling, Elsevier, vol. 51(C), pages 172-182.
    9. Yao, Haixiang & Li, Zhongfei & Li, Duan, 2016. "Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability," European Journal of Operational Research, Elsevier, vol. 252(3), pages 837-851.
    10. Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Mean–variance asset–liability management with asset correlation risk and insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 300-310.
    11. 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.
    12. Haixiang Yao & Xun Li & Zhifeng Hao & Yong Li, 2016. "Dynamic asset–liability management in a Markov market with stochastic cash flows," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1575-1597, October.
    13. Zhang, Miao & Chen, Ping & Yao, Haixiang, 2017. "Mean-variance portfolio selection with only risky assets under regime switching," Economic Modelling, Elsevier, vol. 62(C), pages 35-42.

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