Existence And Uniqueness Of Solutions For FBSDE Driven By A Lévy Process

In the studies of forward-backward stochastic differential equations, there have been many good results. Peng and Wu [10] obtained the existence and uniqueness results of fully coupled forward-backward stochastic differential equations in 1999. In this thesis, we get the theorem of the existence and uniqueness of solutions for FBSDE driven by a Levy process. Not only mathematicians but also financial economists are interested in FBSDE, because FBSDE have important applications in mathematical finance. Many researches have been done about FBSDE driven by Brownian motion or by both Browinan motion and Possion Process. Is it natural to extend such equations to the case of Levy processes? Nualart and Sohoutens [6]established the existence and uniqueness of solutions for BSDE driven by a Levy process of the kind considered in Nualart and Sohoutens [5] with Lipschitz coefficients. The main aims of this thesis is to investigate the existence and uniqueness of solutions for FBSDE driven by a levy process.This thesis is composed of four chapters.Chapter 1: An introduction, state the works of predecessors and the history of question, introduce the main work of this thesis in generally.Chapter 2: Prepared knowledge, include the explanation of notations, related definition. Besides, we also introduce the classical conclusion in the existence and uniqueness of solutions for the following FBSDEand the related knowledge of Levy process.Chapter 3: The proof of existence and uniqueness of solutions for FBSDE. Not only the most important chapter, but also the center of the thesis. In this chapter, we firstly give the following FBSDE driven by a Levy processamongThen we prove the existence and uniqueness of solutions using the method in [10] written by Peng and Wu.Chapter 4: Applications in finance. In conclusion, we investigate a pattern of finance driven by a Levy process. The wealth of investor who starts with some initial endowment ω₀> 0 thusis modeled byOur purpose is to find an optimal strategy to maximize the expected utility of the wealth...