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

Touzi, Nizar; Tan, Xiaolu; Henry-Labordère, Pierre

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

Publisher

Elsevier

Pages

1112-1140

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