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

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

2012-01-31

arxiv.org/abs/1201.6614v1

Mathematics

Probability

Scientific paper

In this paper we show the existence and form uniqueness of a solution for multidimensional backward stochastic differential equations driven by a multidimensional L\'{e}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 L\'{e}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 L\'{e}vy market.

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