Backward stochastic differential equations and Feynman-Kac formula in the presence of jump processes

Thesis Type: Post Graduate

Institution Of The Thesis: Middle East Technical University, Turkey

Approval Date: 2013

Thesis Language: English

Student: Cansu İncegül Yücetürk



Backward Stochastic Differential Equations (BSDEs) appear as a new class of stochastic differential equations, with a given value at the terminal time T. The application area of the BSDEs is conceptually wide which is known only for forty years. In financial mathematics, El Karoui, Peng and Quenez have a fundamental and significant article called “Backward Stochastic Differential Equations in Finance” (1997) which is taken as a groundwork for this thesis. In this thesis we follow the following steps: Firstly, the principal theorems of BSDEs driven by Brownian motion are proved. Later, an application to partial differential equations (PDEs) is presented i.e. generalization of Feynman-Kac formula. Moreover, the studies of Situ in 1997 and his book entitled with “Theory of Stochastic Differential Equations with Jumps and Applications” provide us a framework to prove explicitly the main theorems of BSDEs in the presence of jumps. Afterward, Feynman-Kac formula for general Lévy processes is proven. Lastly, the results are concluded by some applications in financial mathematics.