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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.

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  • 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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