IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v53y2013i1p281-291.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668713000851
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2013.05.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    2. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    3. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 391-401.
    4. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    5. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    6. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    7. Robert Elliott & Tak Kuen Siu, 2009. "On Markov-modulated Exponential-affine Bond Price Formulae," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 1-15.
    8. 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.
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    10. Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2004. "A geometric approach to multiperiod mean variance optimization of assets and liabilities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1079-1113, March.
    11. 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.
    12. 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.
    13. Keel, Alex & Müller, Heinz H., 1995. "Efficient Portfolios in the Asset Liability Context," ASTIN Bulletin, Cambridge University Press, vol. 25(1), pages 33-48, May.
    14. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(4), pages 1125-1152.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    2. Huiling Wu & Chengguo Weng & Yan Zeng, 2018. "Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(2), pages 541-582, March.
    3. Liyuan Wang & Zhiping Chen, 2019. "Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    4. Chen, Kexin & Wong, Hoi Ying, 2019. "Time-consistent mean-variance hedging of an illiquid asset with a cointegrated liquid asset," Finance Research Letters, Elsevier, vol. 29(C), pages 184-192.
    5. 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.
    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. 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.
    8. Wei, Jiaqin & Wang, Tianxiao, 2017. "Time-consistent mean–variance asset–liability management with random coefficients," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 84-96.
    9. Esben Kryger & Maj-Britt Nordfang & Mogens Steffensen, 2020. "Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 405-438, June.
    10. 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.
    11. Georgios I. Papayiannis, 2023. "A Framework for Treating Model Uncertainty in the Asset Liability Management Problem," Papers 2310.11987, arXiv.org.
    12. 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.
    13. 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.
    14. 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.
    15. Chi Kin Lam & Yuhong Xu & Guosheng Yin, 2016. "Dynamic portfolio selection without risk-free assets," Papers 1602.04975, arXiv.org.
    16. Zhang, Jingong & Tan, Ken Seng & Weng, Chengguo, 2017. "Optimal hedging with basis risk under mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 1-15.
    17. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wei, Jiaqin & Wang, Tianxiao, 2017. "Time-consistent mean–variance asset–liability management with random coefficients," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 84-96.
    2. Qian Zhao & Jiaqin Wei & Rongming Wang, 2013. "Mean-Variance Asset-Liability Management with State-Dependent Risk Aversion," Papers 1304.7882, arXiv.org.
    3. Chi Kin Lam & Yuhong Xu & Guosheng Yin, 2016. "Dynamic portfolio selection without risk-free assets," Papers 1602.04975, arXiv.org.
    4. 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.
    5. Li, Yongwu & Li, Zhongfei, 2013. "Optimal time-consistent investment and reinsurance strategies for mean–variance insurers with state dependent risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 86-97.
    6. Zhao, Qian & Shen, Yang & Wei, Jiaqin, 2014. "Consumption–investment strategies with non-exponential discounting and logarithmic utility," European Journal of Operational Research, Elsevier, vol. 238(3), pages 824-835.
    7. Yao, Haixiang & Zeng, Yan & Chen, Shumin, 2013. "Multi-period mean–variance asset–liability management with uncontrolled cash flow and uncertain time-horizon," Economic Modelling, Elsevier, vol. 30(C), pages 492-500.
    8. 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.
    9. 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.
    10. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    11. Xie, Shuxiang & Li, Zhongfei & Wang, Shouyang, 2008. "Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 943-953, June.
    12. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    13. 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.
    14. 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.
    15. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    16. 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.
    17. Alia, Ishak & Chighoub, Farid & Sohail, Ayesha, 2016. "A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 212-223.
    18. 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.
    19. Xiangyu Cui & Xun Li & Duan Li, 2013. "Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection," Papers 1303.1064, arXiv.org.
    20. Chen, Ping & Yam, S.C.P., 2013. "Optimal proportional reinsurance and investment with regime-switching for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 871-883.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:281-291. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.