Stratified regression Monte-Carlo scheme for semilinear PDEs and BSDEs with large scale parallelization on GPUs

Emmanuel Gobet (1) , Jose Lopez-Salas (2) , Plamen Turkedjiev (1) , Carlos Vasquez (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Department of Mathematics, Faculty of Informatics, Universidade da Coruna

In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of the computations on multicore devices such as graphics processing units (GPUs). Our approach consists of a novel method of stratification which appears to be crucial for large scale parallelization.

Keywords: Backward stochastic differential equations; dynamic programming equation; em-pirical regressions; parallel computing; GPUs; CUDA

Domains: Mathematics [math]; Probability [math.PR]

Emmanuel Gobet, Jose Lopez-Salas, Plamen Turkedjiev, Carlos Vasquez. Stratified regression Monte-Carlo scheme for semilinear PDEs and BSDEs with large scale parallelization on GPUs. 2015. ⟨hal-01186000⟩