Backward Stochastic Differential Equations and Feynman-Kac Formula for Levy Processes, with Applications in Finance

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