Backward stochastic differential equations and Feynman-Kac formula for Lévy processes, with applications in finance

David Nualart and Wim Schoutens

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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.

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Bernoulli Volume 7, Number 5 (2001), 761-776.

First available in Project Euclid: 15 March 2004

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backward stochastic differential equations Lévy processes option pricing orthogonal polynomials


Nualart, David; Schoutens, Wim. Backward stochastic differential equations and Feynman-Kac formula for Lévy processes, with applications in finance. Bernoulli 7 (2001), no. 5, 761--776.

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