Simulation of BSDEs by Wiener Chaos Expansion

Philippe Briand (1) , Céline Labart (1)

1 LAMA - Laboratoire de Mathématiques

We present an algorithm to solve BSDEs based on Wiener Chaos Expansion and Picard's iterations. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. We use the Malliavin derivative to compute $Z$. Concerning the error, we derive explicit bounds with respect to the number of chaos and the discretization time step. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.

Mots clés: BSDEs; Wiener Chaos Expansion; simulation

Domaines: Probabilités [math.PR]

Philippe Briand, Céline Labart. Simulation of BSDEs by Wiener Chaos Expansion. The Annals of Applied Probability, 2014, 24 (3), pp.1129-1171. ⟨10.1214/13-AAP943⟩. ⟨hal-00688523v2⟩