arXiv:1201.6614 Abstract | arXiv Analytics

arXiv:1201.6614 [math.PR]Abstract References Reviews Resources

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

Published 2012-01-31Version 1

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.

Categories: math.PR

Subjects: 60H10, 60H15, 60G55

Keywords: backward stochastic differential equations, feynman-kac formula, multidimensional lévy processes, partial differential integral equations, black-scholes partial differential equation

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