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

2012/01/31 by Jianzhong Lin, Lin, Jianzhong
Mathematics · #60G55 #60H10 #60H15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G55 #msc:60H10 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1201.6614

arxiv created 2012/01/31 · arxiv updated 2012/02/01

Abstract

In this paper we show the existence and form uniqueness of a solution for multidimensional backward stochastic differential equations driven by a multidimensional Lévy 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 Lévy 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 Lévy market.

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