Geodesic
Numerical approximation of general Lipschitz BSDEs with branching processes
Bruno Bouchard1 ; Xiaolu Tan1 ; Xavier Warin2
1Université Paris-Dauphine, PSL University, CNRS, UMR [7534], CEREMADE, 75016 PARIS, FRANCE
2EDF R&D & FiME, Laboratoire de Finance des Marchés de l’Energie
ESAIM. Proceedings, Tome 65 (2019), pp. 309-329
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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},
     year = {2019},
     volume = {65},
     doi = {10.1051/proc/201965309},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965309/}
}
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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

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