A decomposition approach for the discrete-time approximation of FBSDEs with a jump
Kharroubi, Idris; Lim, Thomas (2015), A decomposition approach for the discrete-time approximation of FBSDEs with a jump, Random Operators and Stochastic Equations, 23, 2, p. 81-109. 10.1515/rose-2014-0031
TypeArticle accepté pour publication ou publié
Journal nameRandom Operators and Stochastic Equations
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Abstract (EN)We are concerned with the discretization of a solution of a forward-backward stochastic differential equation (FBSDE) with a jump process depending on the Brownian motion. In this paper, we study the cases of Lipschitz generators and the generators with a quadratic growth with respect to the variable z. We propose a recursive scheme based on a general existence result given in the companion paper [Journal of Theoretical Probability 27 (2014), 683–724] and we study the error induced by the time discretization. We prove the convergence of the scheme when the number of time steps n goes to infinity. Our approach allows to get a convergence rate similar to that of schemes of Brownian FBSDEs
Subjects / KeywordsDiscrete-time approximation; forward-backward SDE; Lipschitz generator; decomposition in the reference ltration; progressive enlargement of ltrations
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