A decomposition approach for the discrete-time approximation of BSDEs with a jump II: the quadratic case

TL;DR

This paper develops a convergence analysis for a discrete-time approximation scheme of quadratic FBSDEs with jumps, extending previous work to include jump processes and establishing convergence rates.

Contribution

It introduces a new approach to approximate quadratic FBSDEs with jumps, providing convergence proofs and rates for the scheme as the number of steps increases.

Findings

Proves convergence of the approximation scheme as steps increase

Establishes convergence rate similar to Brownian FBSDE schemes

Handles quadratic growth in the generator with jumps

Abstract

We study the discrete-time approximation for solutions of quadratic forward back- ward stochastic differential equations (FBSDEs) driven by a Brownian motion and a jump process which could be dependent. Assuming that the generator has a quadratic growth w.r.t. the variable z and the terminal condition is bounded, we prove the convergence of the scheme when the number of time steps n goes to infinity. Our approach is based on the companion paper [15] and allows to get a convergence rate similar to that of schemes of Brownian FBSDEs.