Convergence of BSΔEs driven by random walks to BSDEs: The case of (in)finite activity jumps with general driver

Dilip Madan, Martijn Pistorius and Mitja Stadje

Stochastic Processes and their Applications, 2016, vol. 126, issue 5, 1553-1584

Abstract: In this paper we present a weak approximation scheme for BSDEs driven by a Wiener process and an (in)finite activity Poisson random measure with drivers that are general Lipschitz functionals of the solution of the BSDE. The approximating backward stochastic difference equations (BSΔEs) are driven by random walks that weakly approximate the given Wiener process and Poisson random measure. We establish the weak convergence to the solution of the BSDE and the numerical stability of the sequence of solutions of the BSΔEs. By way of illustration we analyze explicitly a scheme with discrete step-size distributions.

Keywords: Backward stochastic differential equation (BSDE); Backward stochastic difference equation (BSΔE); Convergence; Lévy process; Infinite jump-activity (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.11.013

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