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ON NON-ZERO-SUM STOCHASTIC GAME PROBLEMS WITH STOPPING
TIMES
by
Jie Du
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
August 2012
Copyright 2012 Jie Du
Object Description
| Title | On non-zero-sum stochastic game problems with stopping times |
| Author | Du, Jie |
| Author email | jiedu@usc.edu;dujiepku@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2012-05-14 |
| Date submitted | 2012-07-10 |
| Date approved | 2012-07-10 |
| Restricted until | 2012-07-10 |
| Date published | 2012-07-10 |
| Advisor (committee chair) | Zhang, Jianfeng |
| Advisor (committee member) |
Ma, Jin Zapatero, Fernando |
| Abstract | This dissertation consists of three parts. We first study the continuous time non-zero-sum Dynkin game which is a multi-player non-cooperative game on stopping times. We show that the Dynkin game has a Nash equilibrium point for general stochastic processes. The study extends the result of Hamadene and Zhang. ❧ The second part is to study the value dynamics of Dynkin game. In a zero-sum Dynkin game, where one player’s cost is the other player’s benefit, the value process is characterized by a two-barrier reflected backward stochastic differential equation, see Cvitanic and Karatzas. We build a parallel result for non-zero-sum Dynkin game and propose a new form of equilibrium called time-autonomous, which is mainly used to overcome non-uniqueness of the equilibrium. Under this framework, we construct the equivalency relation between a reflected BSDE system with jumps and non-zero-sum Dynkin Game. ❧ Finally we study Principal-Agent problem on stopping times, which addresses time-inconsistent issue in the sense that Bellman’s principle does not hold. We propose a method to solve Principal-Agent problem in discrete time framework. |
| Keyword | Dynkin game; non-zero-sum game; principal-agent problem; stopping time; time inconsistency |
| 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 |
| Contributing entity | University of Southern California |
| Rights | Du, Jie |
| 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_Volume4/etd-DuJie-939.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Full text | ON NON-ZERO-SUM STOCHASTIC GAME PROBLEMS WITH STOPPING TIMES by Jie Du A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) August 2012 Copyright 2012 Jie Du |
