Geodesic
Numerical approximation of general Lipschitz BSDEs with branching processes
Bruno Bouchard1 ; Xiaolu Tan1 ; Xavier Warin2
1 Université Paris-Dauphine, PSL University, CNRS, UMR [7534], CEREMADE, 75016 PARIS, FRANCE
2 EDF R&D & FiME, Laboratoire de Finance des Marchés de l’Energie
ESAIM. Proceedings, Tome 65 (2019), pp. 309-329.

Voir la notice de l'article provenant de la source EDP Sciences

We extend the branching process based numerical algorithm of Bouchard et al. [3], that is dedicated to semilinear PDEs (or BSDEs) with Lipschitz nonlinearity, to the case where the nonlinearity involves the gradient of the solution. As in [3], this requires a localization procedure that uses a priori estimates on the true solution, so as to ensure the well-posedness of the involved Picard iteration scheme, and the global convergence of the algorithm. When, the nonlinearity depends on the gradient, the later needs to be controlled as well. This is done by using a face-lifting procedure. Convergence of our algorithm is proved without any limitation on the time horizon. We also provide numerical simulations to illustrate the performance of the algorithm.
DOI : 10.1051/proc/201965309

Bruno Bouchard 1 ; Xiaolu Tan 1 ; Xavier Warin 2

1 Université Paris-Dauphine, PSL University, CNRS, UMR [7534], CEREMADE, 75016 PARIS, FRANCE
2 EDF R&D & FiME, Laboratoire de Finance des Marchés de l’Energie 
@article{EP_2019_65_a13,
     author = {Bruno Bouchard and Xiaolu Tan and Xavier Warin},
     title = {Numerical approximation of general {Lipschitz} {BSDEs} with branching processes},
     journal = {ESAIM. Proceedings},
     pages = {309--329},
     publisher = {mathdoc},
     volume = {65},
     year = {2019},
     doi = {10.1051/proc/201965309},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965309/}
}
TY  - JOUR
AU  - Bruno Bouchard
AU  - Xiaolu Tan
AU  - Xavier Warin
TI  - Numerical approximation of general Lipschitz BSDEs with branching processes
JO  - ESAIM. Proceedings
PY  - 2019
SP  - 309
EP  - 329
VL  - 65
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201965309/
DO  - 10.1051/proc/201965309
LA  - en
ID  - EP_2019_65_a13
ER  - 
%0 Journal Article
%A Bruno Bouchard
%A Xiaolu Tan
%A Xavier Warin
%T Numerical approximation of general Lipschitz BSDEs with branching processes
%J ESAIM. Proceedings
%D 2019
%P 309-329
%V 65
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201965309/
%R 10.1051/proc/201965309
%G en
%F EP_2019_65_a13
Bruno Bouchard; Xiaolu Tan; Xavier Warin. Numerical approximation of general Lipschitz BSDEs with branching processes. ESAIM. Proceedings, Tome 65 (2019), pp. 309-329. doi : 10.1051/proc/201965309. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965309/

Cité par Sources :