paper

Backward Stochastic Differential Equations and Feynman-Kac Formula for Multidimensional LÃ©vy Processes, with Applications in Finance

arXiv:1201.6614

Abstract

In this paper we show the existence and form uniqueness of a solution for multidimensional backward stochastic differential equations driven by a multidimensional LÃ©vy process with moments of all orders. The results are important from a pure mathematical point of view as well as in the world of finance: an application to Clark-Ocone and Feynman-Kac formulas for multidimensional LÃ©vy processes is presented. Moreover, the Feynman-Kac formula and the related partial differential integral equations provide an analogue of the famous Black-Scholes partial differential equation and thus can be used for the purpose of option pricing in a multidimensional LÃ©vy market.