Weak approximation of second-order BSDEs

Dylan Possamaï (1, 2) , Xiaolu Tan (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL

We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both robustness properties of BSDEs, as proved in Briand, Delyon and Mémin [Stochastic Process. Appl. 97 (2002) 229–253], and tightness of solutions to discrete time BSDEs. In particular, when the approximating martingales are given by some particular controlled Markov chains, we obtain several concrete numerical schemes for 2BSDEs, which we illustrate on specific examples.

Mots clés: Second order BSDEs; weak approximation; numerical scheme; robustness of BSDE

Domaines: Probabilités [math.PR]

Dylan Possamaï, Xiaolu Tan. Weak approximation of second-order BSDEs. The Annals of Applied Probability, 2015, 25 (5), pp.2535-2562. ⟨10.1214/14-AAP1055⟩. ⟨hal-01102789⟩