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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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    References listed on IDEAS

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    8. Consiglio, Andrea & Cocco, Flavio & Zenios, Stavros A., 2008. "Asset and liability modelling for participating policies with guarantees," European Journal of Operational Research, Elsevier, vol. 186(1), pages 380-404, April.
    9. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2006. "A path integral approach to asset-liability management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 404-416.
    10. Chen, Ping & Yang, Hailiang & Yin, George, 2008. "Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 456-465, December.
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    Citations

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    Cited by:

    1. Yao, Haixiang & Yang, Zhou & Chen, Ping, 2013. "Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 851-863.
    2. 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.
    3. 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.
    4. 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.
    5. repec:bpj:jossai:v:5:y:2017:i:3:p:229-249:n:3 is not listed on IDEAS
    6. repec:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9266-z is not listed on IDEAS
    7. Chang, Hao, 2015. "Dynamic mean–variance portfolio selection with liability and stochastic interest rate," Economic Modelling, Elsevier, vol. 51(C), pages 172-182.
    8. 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.
    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. repec:eee:insuma:v:77:y:2017:i:c:p:177-188 is not listed on IDEAS
    11. 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.

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