A numerical algorithm for a class of BSDE via branching process.

Summary We generalize the algorithm for semi-linear parabolic PDEs in Henry-Labordére \cite{Henry-Labordere_branching} 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, Keller, Touzi and Zhang \cite{EkrenKellerTouziZhang} and extended in Ekren, Touzi and Zhang \cite{EkrenTouziZhang1, EkrenTouziZhang2}.