Numerical approximation of Backward Stochastic Differential Equations with Jumps

Antoine Lejay (1, 2) , Ernesto Mordecki (3) , Soledad Torres (4)

1 TOSCA - TO Simulate and CAlibrate stochastic models
2 IECL - Institut Élie Cartan de Lorraine
3 CMAT - Centro de Matemática [Montevideo]
4 Departamento de Estadistica [Valparaiso]

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.

Mots clés: Backward SDEs with jumps; Skorokhod topology; Poisson Process; Monte Carlo method

Domaines: Probabilités [math.PR]

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⟩