Abstract
Abstract This paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under linear growth generator, we prove existence and uniqueness of solution.
Highlights
It is well known that Backward stochastic differential equations (BSDEs in short) driven by random Poisson measure are natural extension of classical BSDEs
These equations, first discussed by Tang and Li [8] can be seen as a generalization of Pardoux and Peng’s work [6], which constitute the key point of solving problem in financial mathematics and studying non linear partial differential equations (PDEs in short) by means of stochastic tools
Among them we mention the result of Barles et al [1] who establish a probabilistic interpretation of a solution of a partial differential equation (PIDE)
Summary
It is well known that Backward stochastic differential equations (BSDEs in short) driven by random Poisson measure are natural extension of classical BSDEs. Some authors studying parabolic integral-partial differential equation (PIDE), interested in BSDEs with Poisson Process (BSDEP in short). Among others Mao [3] investigate successfully these equations with the Osgood condition. This one is introduced by specific function which allows the use of the well known Bihari’s Lemma to get uniqueness. They prove an existence and uniqueness result when the generator satisfies the Osgood condition. In this work we interested in extending this result to multidimensional BSDEs driven by random Poisson measure (MBSDEPs in short) satisfying the Osgood condition. Inspired by the method introduced by Fan et al [2], we prove existence and uniqueness of solution of a MBSDEP.
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