A regression Monte-Carlo method for Backward Doubly Stochastic Differential Equations

TL;DR

This paper extends regression Monte-Carlo methods to backward doubly stochastic differential equations, providing a numerical approximation scheme for these complex equations.

Contribution

It adapts existing regression Monte-Carlo techniques to the setting of backward doubly stochastic differential equations, expanding their applicability.

Findings

Proposes a new numerical approximation scheme for backward doubly stochastic differential equations.

Extends regression Monte-Carlo methods from backward stochastic to backward doubly stochastic equations.

Provides theoretical foundation for numerical solutions of these equations.

Abstract

This paper extends the idea of E.Gobet, J.P.Lemor and X.Warin from the setting of Backward Stochastic Differential Equations to that of Backward Doubly Stochastic Differential equations. We propose some numerical approximation scheme of these equations introduced by E.Pardoux and S.Peng.