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A numerical algorithm for a class of BSDEs via the branching process

Touzi, Nizar; Tan, Xiaolu; Henry-Labordère, Pierre (2014), A numerical algorithm for a class of BSDEs via the branching process, Stochastic Processes and their Applications, 124, 2, p. 1112-1140. http://dx.doi.org/10.1016/j.spa.2013.10.005

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1302.4624v3
Date
2014
Journal name
Stochastic Processes and their Applications
Volume
124
Number
2
Publisher
Elsevier
Pages
1112-1140
Publication identifier
http://dx.doi.org/10.1016/j.spa.2013.10.005
Metadata
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Author(s)
Touzi, Nizar
Tan, Xiaolu
Henry-Labordère, Pierre
Abstract (EN)
We give a study to the algorithm for semi-linear parabolic PDEs in Henry-Labordère (2012) and then generalize it to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution of BSDEs, we use the notion of viscosity solution of path dependent PDEs introduced by Ekren et al. (2013) [5] and extended in Ekren et al. (2013) [6] and [7].
Subjects / Keywords
Path dependent PDEs; Viscosity solution; Branching process; BSDEs; Numerical algorithm

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