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

Haixiang Yao, Zhongfei Li and Shumin Chen

Economic Modelling, 2014, vol. 36, issue C, 244-251

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.

Keywords: Continuous time mean–variance; Hamilton–Jacobi–Bellman equation; Portfolio selection; Dynamic programming; Two-fund separation theorem (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecmode:v:36:y:2014:i:c:p:244-251

DOI: 10.1016/j.econmod.2013.09.041

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