Indefinite stochastic LQ control with financial applications.
As we know, the deterministic LQ problems are well-posed if the state weighting matrix and the control weighting matrix are nonnegative and positive definite in the cost function, respectively. Some practical problems, however, often include indefinite weighting matrices in their cost functions such...
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| Format: | Others |
| Language: | English Chinese |
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2000
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| Online Access: | http://library.cuhk.edu.hk/record=b6073917 http://repository.lib.cuhk.edu.hk/en/item/cuhk-342986 |
| Summary: | As we know, the deterministic LQ problems are well-posed if the state weighting matrix and the control weighting matrix are nonnegative and positive definite in the cost function, respectively. Some practical problems, however, often include indefinite weighting matrices in their cost functions such as mean-variance portfolio selection problem. This inspires us to further study the indefinite LQ problems in detail. === In this thesis, we study indefinite stochastic linear-quadratic (LQ) control with jumps and present some financial applications of this new development. === The results of the above LQ control problems are employed to deal with a mean-variance portfolio selection model in an incomplete financial market. An optimal analytical investment strategy is directly derived and the expression of its risk is explicitly presented. In addition, a mean-variance portfolio selection model in a financial market where shorting is not allowed is investigated in detail via the stochastic LQ problem with nonnegative controls. In particular, the explicit expression of the efficient frontier enables an investor to better understand the relation between the expected terminal wealth and the risk in a stock market with no-shorting. === The weighting matrices in the cost function are allowed to be indefinite (in particular, negative) when the diffusion term linearly depends on the control variable in the state equation. In this case, indefinite stochastic LQ control problems with jumps may still be sensible and well-posed. In an infinite time horizon, solvability of coupled generalized algebraic Riccati equations (CGAREs) is sufficient for the well-posedness of the stochastic LQ control problem with jumps. Moreover, an approach algorithm is devised to solve the CGAREs via semi-definite programming over linear matrix inequalities. On the other hand, it is shown that the well-posedness of the stochastic LQ control problem in a finite time horizon with jumps is equivalent to solvability of coupled generalized Riccati equations. === Li Xun. === "November 2000." === Advisers: Cai Xiaoqiang; Zhou Xunyu. === Source: Dissertation Abstracts International, Volume: 61-10, Section: B, page: 5541. === Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. === Includes bibliographical references (p. 115-122). === 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 dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Abstracts in English and Chinese. === School code: 1307. |
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