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

Idris Kharroubi (1) , Thomas Lim (2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LAP - Laboratoire Analyse et Probabilités
3 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise

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.

Keywords: decomposition in the reference filtration; Discrete-time approximation; forward-backward SDE with a jump; generator of quadratic growth; progressive enlargement of filtrations; decomposition in the reference filtration.

Domains: Optimization and Control [math.OC]

Idris Kharroubi, Thomas Lim. A decomposition approach for the discrete-time approximation of BSDEs with a jump II: the quadratic case. 2012. ⟨hal-00757426⟩