Continuous-time mean–variance portfolio selection with only risky assets
AbstractWe 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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Bibliographic InfoArticle provided by Elsevier in its journal Economic Modelling.
Volume (Year): 36 (2014)
Issue (Month): C ()
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Web page: http://www.elsevier.com/locate/inca/30411
Continuous time mean–variance; Hamilton–Jacobi–Bellman equation; Portfolio selection; Dynamic programming; Two-fund separation theorem;
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