Quasi-Regression Monte-Carlo Scheme for Semi-Linear PDEs and BSDEs with Large Scale Parallelization on GPUs

  • Emmanuel Gobet
  • José Germán López-SalasEmail author
  • Carlos Vázquez
Original Paper


In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations, and we analyze the convergence of the proposed method. The algorithm also approximates the solution to the related semi-linear parabolic partial differential equation obtained through the well known Feynman–Kac representation. For the sake of enriching the algorithm with high order convergence a weighted approximation of the solution is computed and appropriate conditions on the parameters of the method are inferred. With the challenge of tackling problems in high dimensions we propose suitable projections of the solution and efficient parallelizations of the algorithm taking advantage of powerful many core processors such as graphics processing units.

Mathematics Subject Classification

49L20 62Jxx 65C30 93E24 68W10 


Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© CIMNE, Barcelona, Spain 2019

Authors and Affiliations

  1. 1.Centre de Mathématiques AppliquéesÉcole Polytechnique and CNRSPalaiseau CedexFrance
  2. 2.Department of Mathematics, Faculty of InformaticsUniversidade da CoruñaA CoruñaSpain

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