Key Words: continuous-time model, mean-variance, transaction costs, stochastic singular control, Lagrange multiplier method, parabolic free-boundary problem, double-obstacle problem, Skorokhod problem. / We study continuous-time Markowitz's mean-variance portfolio selection problem in a market with one stock, one bond and proportional transaction costs. The presence of transaction costs makes the problem being a singular control problem in a finite time horizon, which is very hard to deal with from the point view of control theory. Using a partial differential equation approach, we formulate the problem as a double obstacle problem, and prove the smoothness of the value function. Then we give the necessary and sufficient conditions for the existence of an optimal solution and completely characterize the optimal strategy when the problem is feasible. We show three critical distinctive features of the Markowitz model under the presence of transaction costs. First, the expected return on the portfolio could be too high to achieve if the time to maturity is not long enough, while without transaction costs, any expected return can be reached in an arbitrary short time. Second, instead of keeping the investment ratio between stock and bond to be a constant, there exists time-dependent upper and lower boundaries, transaction is carried out only if the investment ratio is on the boundaries. Third, there exists a critical time, which only depends on the market parameters, such that beyond the time no more investment will be added to stock holding. Our result is closer to real investment practice where people tend not to invest on risky assets towards the end of the investment horizon. / Xu Zuoquan. / "January 2007." / Adviser: Xunyu Zhou. / Source: Dissertation Abstracts International, Volume: 68-08, Section: B, page: 5290. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 118-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343812 |
| Date | January 2007 |
| Contributors | Xu, Zuoquan, Chinese University of Hong Kong Graduate School. Division of Systems Engineering and Engineering Management. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (xi, 123 p. : ill.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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