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Numerical approximation of doubly reflected BSDEs with jumps and RCLL obstacles

Dumitrescu, Roxana; Labart, Céline (2016), Numerical approximation of doubly reflected BSDEs with jumps and RCLL obstacles, Journal of Mathematical Analysis and Applications, 442, 1, p. 206-243. 10.1016/j.jmaa.2016.03.044

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1406.3612v1
Date
2016
Journal name
Journal of Mathematical Analysis and Applications
Volume
442
Number
1
Publisher
Academic Press
Published in
Paris
Pages
206-243
Publication identifier
10.1016/j.jmaa.2016.03.044
Metadata
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Author(s)
Dumitrescu, Roxana

Labart, Céline
Abstract (EN)
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.
Subjects / Keywords
penalization method; Backward stochastic differential equations with jumps; Double barrier reflected BSDEs

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