Convergence of BSΔEs driven by random walks to BSDEs: the case of
(in)finite activity jumps with general driver
(in)finite activity jumps with general driver
File(s)BSDeltaE_rev_0311final.pdf (445.21 KB)
Accepted version
Author(s)
Madan, D
Pistorius, M
Stadje, M
Type
Journal Article
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 (BS\Delta Es) 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 BS\Delta Es. By
way of illustration we analyse explicitly a scheme with discrete step-size
distributions.
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 (BS\Delta Es) 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 BS\Delta Es. By
way of illustration we analyse explicitly a scheme with discrete step-size
distributions.
Date Issued
2015-12-17
Date Acceptance
2015-11-29
Citation
Stochastic Processes and Their Applications, 2015, 126 (5), pp.1553-1584
ISSN
0304-4149
Publisher
Elsevier
Start Page
1553
End Page
1584
Journal / Book Title
Stochastic Processes and Their Applications
Volume
126
Issue
5
Copyright Statement
© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
math.PR
math.PR
60H10, 60Fxx
Publication Status
Published