Continuous-Time Mean-Variance Portfolio Selection with Bankruptcy Prohibition

32 Pages Posted: 23 Mar 2005

See all articles by Tomasz R. Bielecki

Tomasz R. Bielecki

Illinois Institute of Technology

Hanqing Jin

Chinese University of Hong Kong

Stanley R. Pliska

University of Illinois at Chicago - Department of Finance

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Abstract

A continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options.

Suggested Citation

Bielecki, Tomasz R. and Jin, Hanqing and Pliska, Stanley R. and Zhou, Xun Yu, Continuous-Time Mean-Variance Portfolio Selection with Bankruptcy Prohibition. Available at SSRN: https://ssrn.com/abstract=687241

Tomasz R. Bielecki

Illinois Institute of Technology ( email )

Department of Applied Mathematics
10 W. 32nd Street
Chicago, IL 60616
United States
312 567 3185 (Phone)
312 567 3135 (Fax)

Hanqing Jin

Chinese University of Hong Kong ( email )

Hong Kong
Hong Kong

Stanley R. Pliska (Contact Author)

University of Illinois at Chicago - Department of Finance ( email )

2431 University Hall (UH)
601 S. Morgan Street
Chicago, IL 60607-7124
United States
312-996 7170 (Phone)

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong
852 2609-8320 (Phone)
852 2603-5505 (Fax)

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