Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles

TL;DR

This paper presents a new fully implementable discrete scheme for solving doubly reflected BSDEs with jumps, avoiding penalization and providing convergence proofs and numerical examples.

Contribution

It introduces a direct discretization method for DRBSDEs with jumps that depends only on the number of time steps, improving upon previous penalization-based schemes.

Findings

The scheme converges as the number of steps increases.

Numerical examples demonstrate the scheme's effectiveness.

The method is fully implementable and avoids penalization parameters.

Abstract

We introduce a discrete time reflected scheme to solve doubly reflected Backward Stochastic Differential Equations with jumps (in short DRBSDEs), driven by a Brownian motion and an independent compensated Poisson process. As in Dumitrescu-Labart (2014), we approximate the Brownian motion and the Poisson process by two random walks, but contrary to this paper, we discretize directly the DRBSDE, without using a penalization step. This gives us a fully implementable scheme, which only depends on one parameter of approximation: the number of time steps $n$ (contrary to the scheme proposed in Dumitrescu-Labart (2014), which also depends on the penalization parameter). We prove the convergence of the scheme, and give some numerical examples.