Numerical approximation of doubly reflected BSDEs with jumps and RCLL obstacles

TL;DR

This paper develops a numerical scheme for solving doubly reflected BSDEs with jumps, using binomial trees and penalization, and demonstrates its convergence and effectiveness through numerical examples.

Contribution

It introduces an implementable discrete approximation scheme for DBBSDEs with jumps, incorporating RCLL obstacles and Mokobodski's condition, and proves its convergence.

Findings

The scheme converges to the true solution of the DBBSDE.

Numerical examples validate the theoretical convergence and applicability.

The method effectively handles general jumps in the process.

Abstract

We study a discrete time approximation scheme for the solution of a doubly reflected Backward Stochastic Differential Equation (DBBSDE in short) with jumps, driven by a Brownian motion and an independent compensated Poisson process. Moreover, we suppose that the obstacles are right continuous and left limited (RCLL) processes with predictable and totally inaccessible jumps and satisfy Mokobodski's condition. Our main contribution consists in the construction of an implementable numerical sheme, based on two random binomial trees and the penalization method, which is shown to converge to the solution of the DBBSDE. Finally, we illustrate the theoretical results with some numerical examples in the case of general jumps.