IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v36y2014icp244-251.html
   My bibliography  Save this article

Continuous-time mean–variance portfolio selection with only risky assets

Author

Listed:
  • Yao, Haixiang
  • Li, Zhongfei
  • Chen, Shumin

Abstract

We investigate in this paper a continuous-time mean–variance portfolio selection problem in a general market setting with multiple assets that all can be risky. Using the Lagrange duality method and the dynamic programming approach, we derive explicit closed-form expressions for the efficient investment strategy and the mean–variance efficient frontier. We provided a necessary and sufficient condition under which the global minimum variance is zero and there exists a risk-free wealth process. Our results reveal that, even if there is no risk-free asset in the market, there can still exist a risk-free wealth process, the global minimum variance can be zero, and the efficient frontier can be a straight line in the mean–standard derivation plane. In addition, we further prove the validity of the two-fund separation theorem.

Suggested Citation

  • Yao, Haixiang & Li, Zhongfei & Chen, Shumin, 2014. "Continuous-time mean–variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 36(C), pages 244-251.
    • Handle: RePEc:eee:ecmode:v:36:y:2014:i:c:p:244-251
    DOI: 10.1016/j.econmod.2013.09.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S026499931300401X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2013.09.041?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. Viceira, Luis M., 2012. "Bond risk, bond return volatility, and the term structure of interest rates," International Journal of Forecasting, Elsevier, vol. 28(1), pages 97-117.
    2. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. LuisM. Viceira & John Y. Campbell, 2001. "Who Should Buy Long-Term Bonds?," American Economic Review, American Economic Association, vol. 91(1), pages 99-127, March.
    5. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    6. Xie, Shuxiang, 2009. "Continuous-time mean-variance portfolio selection with liability and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 148-155, August.
    7. 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.
    8. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    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. Chiu, Mei Choi & Wong, Hoi Ying, 2011. "Mean-variance portfolio selection of cointegrated assets," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1369-1385, August.
    11. 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.
    12. Jianming Xia & Jia‐An Yan, 2006. "Markowitz'S Portfolio Optimization In An Incomplete Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 203-216, January.
    13. 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.
    14. Markus Leippold & Fabio Trojani & Paolo Vanini, 2011. "Multiperiod mean-variance efficient portfolios with endogenous liabilities," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1535-1546.
    15. Chun Hung Chiu & Xun Yu Zhou, 2011. "The premium of dynamic trading," Quantitative Finance, Taylor & Francis Journals, vol. 11(1), pages 115-123.
    16. Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alex, 2010. "On mean-variance portfolio selection under a hidden Markovian regime-switching model," Economic Modelling, Elsevier, vol. 27(3), pages 678-686, May.
    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. Aleš Černý & Christoph Czichowsky & Jan Kallsen, 2024. "Numeraire-Invariant Quadratic Hedging and Mean–Variance Portfolio Allocation," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 752-781, May.
    2. Pfiffelmann, Marie & Roger, Tristan & Bourachnikova, Olga, 2016. "When Behavioral Portfolio Theory meets Markowitz theory," Economic Modelling, Elsevier, vol. 53(C), pages 419-435.
    3. Pun, Chi Seng, 2018. "Time-consistent mean-variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 75(C), pages 281-292.
    4. Legendre, François & Togola, Djibril, 2016. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Economic Modelling, Elsevier, vol. 58(C), pages 627-641.
    5. 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.
    6. 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.
    7. Adibi, Nabiollah & Ataee-pour, Majid, 2015. "Decreasing minerals׳ revenue risk by diversification of mineral production in mineral rich countries," Resources Policy, Elsevier, vol. 45(C), pages 121-129.
    8. Zhang, Caibin & Liang, Zhibin, 2022. "Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    9. Lord Mensah, 2016. "Asset Allocation Brewed Accross African Stock Markets," Proceedings of Economics and Finance Conferences 3205757, International Institute of Social and Economic Sciences.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. 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.
    9. Chang, Hao, 2015. "Dynamic mean–variance portfolio selection with liability and stochastic interest rate," Economic Modelling, Elsevier, vol. 51(C), pages 172-182.
    10. Ying Hu & Xiaomin Shi & Zuo Quan Xu, 2022. "Non-homogeneous stochastic LQ control with regime switching and random coefficients," Papers 2201.01433, arXiv.org, revised Jul 2023.
    11. Ryle S. Perera, 2020. "Provisions for bank deposit withdrawals and portfolio selection," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-32, March.
    12. Liang, Zongxia & Zhao, Xiaoyang, 2016. "Optimal mean–variance efficiency of a family with life insurance under inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 164-178.
    13. 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.
    14. Pun, Chi Seng, 2018. "Time-consistent mean-variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 75(C), pages 281-292.
    15. Wang, Ning & Zhang, Yumo, 2024. "Robust asset-liability management games for n players under multivariate stochastic covariance models," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 67-98.
    16. Zhang, Caibin & Liang, Zhibin, 2022. "Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    17. 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.
    18. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.
    19. 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.
    20. 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.

    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:ecmode:v:36:y:2014:i:c:p:244-251. 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/30411 .

    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.