In this paper we show the existence and uniqueness of a solution for backward stochastic differential equations driven by a Lévy process with moments of all orders. The results are important from a pure mathematical point of view as well as in finance: an application to Clark-Ocone and Feynman-Kac formulas for Lévy processes is presented. Moreover, the Feynman-Kac formula and the related partial differential integral equation provide an analogue of the famous Black-Scholes partial differential equation and thus can be used for the purpose of option pricing in a Lévy market.
"Backward stochastic differential equations and Feynman-Kac formula for Lévy processes, with applications in finance." Bernoulli 7 (5) 761 - 776, October 2001.