Numerical approximation of doubly reflected BSDEs with jumps and RCLL obstacles
Probability
2016-12-14 v2
Abstract
We study a discrete time approximation scheme for the solution of a doubly reflected Backward Stochastic Differential Equation (DBBSDE in short) with jumps, driven by a Brownian motion and an independent compensated Poisson process. Moreover, we suppose that the obstacles are right continuous and left limited (RCLL) processes with predictable and totally inaccessible jumps and satisfy Mokobodski's condition. Our main contribution consists in the construction of an implementable numerical sheme, based on two random binomial trees and the penalization method, which is shown to converge to the solution of the DBBSDE. Finally, we illustrate the theoretical results with some numerical examples in the case of general jumps.
Keywords
Cite
@article{arxiv.1406.3612,
title = {Numerical approximation of doubly reflected BSDEs with jumps and RCLL obstacles},
author = {Roxana Dumitrescu and Céline Labart},
journal= {arXiv preprint arXiv:1406.3612},
year = {2016}
}