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Weak approximation of second-order BSDEs

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

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Type
Article accepté pour publication ou publié
Date
2015
Journal name
The Annals of Applied Probability
Volume
25
Number
5
Publisher
Institute of Mathematical Statistics
Pages
2535-2562
Publication identifier
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Author(s)
Possamaï, Dylan
Tan, Xiaolu
Abstract (EN)
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.
Subjects / Keywords
robustness of BSDE; numerical scheme; weak approximation; Second order BSDEs