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Keywords:

backward stochastic differential equations, levy processes, option pricing, orthogonal polynomials, Science & Technology, Physical Sciences, Statistics & Probability, Mathematics, Levy processes, 0104 Statistics, 1403 Econometrics, 4905 Statistics

Abstract:

In this paper we show the existence and uniqueness of a solution for backward stochastic differential equations driven by a Levy 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 Feymnan-Kac formulas for Levy 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 Levy market.