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DYNAMIC EQUILIBRIUM MODEL FOR LIMIT ORDER BOOK AND
OPTIMAL EXECUTION PROBLEM
by
Xinyang Wang
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
August 2011
Copyright 2011 Xinyang Wang
Object Description
| Title | Dynamic equilibrium model for limit order book and optimal execution problem |
| Author | Wang, Xinyang |
| Author email | randomlove.pku@gmail.com;xinyang.la@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2011-06-13 |
| Date submitted | 2011-07-11 |
| Date approved | 2011-07-13 |
| Restricted until | 2011-07-13 |
| Date published | 2011-07-13 |
| Advisor (committee chair) | Ma, Jin |
| Advisor (committee member) |
Zhang, Jianfeng Zapatero, Fernando |
| Abstract | In this dissertation we study the optimal execution problem on an order driven market under our equilibrium model for the limit order book (LOB). In our model the dynamics of the price of a financial security can be decomposed into two independent elements, the fundamental price and the supply / demand of the market. The main feature of our model is that the shape of the LOB can be determined endogenously by an expected return function via a competitive equilibrium argument. The resulting equilibrium distribution is random, nonlinear, and time inhomogeneous. Thus the liquidity cost and the price impact of large trades are self-contained in our model, and can be dynamically defined in a natural way. Assuming the zero resilience, we argue that the liquidity cost should be essentially linear with respect to the instantaneous trade size. As a consequence, we show that the optimization problem could be formulated as a special finite-fuel type of singular stochastic control problem. We verify the Dynamic Programming Principle (DPP) in this case, and prove that the value function is a viscosity solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation, which is in the form of a quasi-integro-variational inequality (QIVI) as expected. We then construct the optimal portfolio strategy using the classical solution to the HJB equation, and it turns out to contain both singular and regular continuous parts. We conclude the work and make remarks on some topics for future research at the end. |
| Keyword | limit order book; liquidity risk; optimal execution |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | Wang, Xinyang |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume71/etd-WangXinyan-76.pdf |
Description
| Title | Page 1 |
| Full text | DYNAMIC EQUILIBRIUM MODEL FOR LIMIT ORDER BOOK AND OPTIMAL EXECUTION PROBLEM by Xinyang Wang A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) August 2011 Copyright 2011 Xinyang Wang |
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