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

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  • 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
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Pfiffelmann, Marie & Roger, Tristan & Bourachnikova, Olga, 2016. "When Behavioral Portfolio Theory meets Markowitz theory," Economic Modelling, Elsevier, vol. 53(C), pages 419-435.
    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. Lord Mensah, 2016. "Asset Allocation Brewed Accross African Stock Markets," Proceedings of Economics and Finance Conferences 3205757, International Institute of Social and Economic Sciences.
    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. 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.
    6. 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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