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Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach

Author

Listed:
  • Wei, J.
  • Wong, K.C.
  • Yam, S.C.P.
  • Yung, S.P.

Abstract

In this article, we provide the first study in the time consistent solution of the mean–variance asset–liability management (MVALM). The framework is even considered under a continuous time Markov regime-switching setting. Using the extended Hamilton–Jacobi–Bellman equation (HJB) (see Björk and Murgoci (2010)), we show that the time consistent equilibrium control is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the similar problem in Björk and Murgoci (2010), in which it is independent of the state. Finally, we give a numerical comparison between our work with the corrected version (as obtained here) of pre-commitment strategy in Chen et al. (2008).

Suggested Citation

  • Wei, J. & Wong, K.C. & Yam, S.C.P. & Yung, S.P., 2013. "Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 281-291.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:281-291
    DOI: 10.1016/j.insmatheco.2013.05.008
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    References listed on IDEAS

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    1. Ping Chen & Hailiang Yang, 2011. "Markowitz's Mean-Variance Asset-Liability Management with Regime Switching: A Multi-Period Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(1), pages 29-50.
    2. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    8. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    9. 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.
    10. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    11. Chiu, Mei Choi & Li, Duan, 2006. "Asset and liability management under a continuous-time mean-variance optimization framework," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 330-355, December.
    12. Keel, Alex & Müller, Heinz H., 1995. "Efficient Portfolios in the Asset Liability Context," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 25(01), pages 33-48, May.
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    Citations

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    Cited by:

    1. Wu, Huiling & Chen, Hua, 2015. "Nash equilibrium strategy for a multi-period mean–variance portfolio selection problem with regime switching," Economic Modelling, Elsevier, vol. 46(C), pages 79-90.
    2. A. Bensoussan & K. Sung & S. Yam, 2013. "Linear–Quadratic Time-Inconsistent Mean Field Games," Dynamic Games and Applications, Springer, vol. 3(4), pages 537-552, December.
    3. Wong, Tat Wing & Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Time-consistent mean–variance hedging of longevity risk: Effect of cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 56-67.
    4. repec:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9266-z is not listed on IDEAS
    5. repec:spr:orspec:v:40:y:2018:i:2:d:10.1007_s00291-017-0502-2 is not listed on IDEAS
    6. Chi Kin Lam & Yuhong Xu & Guosheng Yin, 2016. "Dynamic portfolio selection without risk-free assets," Papers 1602.04975, arXiv.org.
    7. repec:eee:insuma:v:75:y:2017:i:c:p:1-15 is not listed on IDEAS
    8. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    9. repec:eee:insuma:v:77:y:2017:i:c:p:84-96 is not listed on IDEAS
    10. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.

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