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FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
WITH DISCONTINUOUS COEFFICIENT AND REGIME SWITCHING
TERM STRUCTURE MODEL
by
Jianfu Chen
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)
May 2011
Copyright 2011 Jianfu Chen
Object Description
| Title | Forward-backward stochastic differential equations with discontinuous coefficient and regime switching term structure model |
| Author | Chen, Jianfu |
| Author email | kennethcjf@gmail.com; jianfuch@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2011-01-10 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-03-24 |
| Advisor (committee chair) | Ma, Jin |
| Advisor (committee member) |
Zhang, Jianfeng Zapatero, Fernando |
| Abstract | In this dissertation, we propose a regime switch term structure model built as forward-backward stochastic differential equations. We first generalize the model and study the forward-backward SDEs with discontinuous coefficients. Generally speaking, we adopt the tactics of the Four-Step scheme as our strategy of finding the solution. First, we find a solution v to the PDE associated with the FBSDEs. Then we use this v to decouple the FBSDEs, and solve each equation individually. A weak solution was successfully found. We then returned to the term structure model. We apply the framework of analysis from the general model to the regime switch term structure model, with some minor modifications. A solution, slightly weaker than the general case, was found for the term structure model, as well as the explicit relationship between the short rate and the long term bond price, all of which confirmed our model is fairly well-grounded. Numerical experiments were also conducted to show the validity of our theory. Results are rather satisfactory, providing us with strong empirical support. |
| Keyword | discontinuous coefficient; regime switching; stochastic differential equations |
| 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-m3696 |
| Rights | Chen, Jianfu |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Chen-4264 |
| Archival file | uscthesesreloadpub_Volume14/etd-Chen-4264.pdf |
Description
| Title | Page 1 |
| Full text | FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS COEFFICIENT AND REGIME SWITCHING TERM STRUCTURE MODEL by Jianfu Chen 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) May 2011 Copyright 2011 Jianfu Chen |
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