Page 1 |
Save page Remove page | Previous | 1 of 86 | Next |
|
small (250x250 max)
medium (500x500 max)
Large (1000x1000 max)
Extra Large
large ( > 500x500)
Full Resolution
All (PDF)
|
This page
All
|
EQUILIBRIUM MODEL OF LIMIT ORDER BOOK AND OPTIMAL
EXECUTION PROBLEM
by
Eunjung Noh
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 2018
Copyright 2018 Eunjung Noh
Object Description
| Title | Equilibrium model of limit order book and optimal execution problem |
| Author | Noh, Eunjung |
| Author email | eunjungn@usc.edu;jennynoh86@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2018-05-21 |
| Date submitted | 2018-08-10 |
| Date approved | 2018-08-10 |
| Restricted until | 2018-08-10 |
| Date published | 2018-08-10 |
| Advisor (committee chair) | Ma, Jin |
| Advisor (committee member) |
Zhang, Jianfeng Lv, Jinchi Mikulevicius, Remigijus Lototsky, Sergey |
| Abstract | In this dissertation, we study an equilibrium model of a limit order book (LOB) and an optimal execution problem. To generalize the previous results, we accommodate the idea of Bertrand price competition, as well as nonlocal mean-field stochastic differential equation (SDE) with evolving intensity and reflecting boundary conditions. To describe the equilibrium of LOB, we start with N sellers’ static Bertrand game, and extend the model to continuous time setting to formulate it as a mean-field type control problem of the representative seller, who wants to maximize the discounted lifelong expected utility. Using dynamic programming principle (DPP), we could form a Hamilton-Jacobi-Bellman (HJB) equation and prove the value function is the viscosity solution of it. And, we show the value function can be used to obtain the equilibrium density function of a LOB. ❧ Assuming the LOB has reached at the equilibrium, we solve the optimal execution problem of a buyer, who wants to purchase a certain number of shares during the finite time horizon with minimum cost. Again, we show that the Bellman principle of DPP holds in this case, and the value function is the viscosity solution of the HJB quasi-variational inequality (QVI). Also, we investigate the optimal strategy when the QVI has a classical solution. |
| Keyword | limit order book; optimal execution; equilibrium; Bertrand model; mean-field SDE with jump and reflecting boundary condition; discontinuous Skorohod problem; stochastic control |
| Language | English |
| Format (imt) | application/pdf |
| 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 |
| Contributing entity | University of Southern California |
| Rights | Noh, Eunjung |
| Physical access | 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@lib.usc.edu |
| Filename | etd-NohEunjung-6728.pdf |
| Archival file | Volume3/etd-NohEunjung-6728.pdf |
Description
| Title | Page 1 |
| Full text | EQUILIBRIUM MODEL OF LIMIT ORDER BOOK AND OPTIMAL EXECUTION PROBLEM by Eunjung Noh 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 2018 Copyright 2018 Eunjung Noh |
