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Numerical approximation of Backward Stochastic Differential Equations with Jumps

Abstract : In this paper we propose a numerical method to approximate the solution of a Backward Stochastic Differential Equations with Jumps (BSDEJ). This method is based on the construction of a discrete BSDEJ driven by a complete system of three orthogonal discrete time-space martingales, the first a random walk converging to a Brownian motion; the second, another random walk, independent of the first one, converging to a Poisson process. The solution of this discrete BSDEJ is shown to weakly converge to the solution of the continuous time BSDEJ. An application to partial integro-differential equations is given.
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Submitted on : Thursday, September 18, 2014 - 7:40:52 AM
Last modification on : Friday, January 21, 2022 - 3:20:00 AM
Long-term archiving on: : Friday, December 19, 2014 - 10:50:34 AM

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  • HAL Id : inria-00357992, version 4

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Antoine Lejay, Ernesto Mordecki, Soledad Torres. Numerical approximation of Backward Stochastic Differential Equations with Jumps. [Research Report] RR-8595, INRIA. 2014, pp.32. ⟨inria-00357992v4⟩

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