Annals of Applied Probability

Weak approximation of second-order BSDEs

Dylan Possamaï and Xiaolu Tan

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 25, Number 5 (2015), 2535-2562.

Dates
Received: September 2013
Revised: May 2014
First available in Project Euclid: 30 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1438261048

Digital Object Identifier
doi:10.1214/14-AAP1055

Mathematical Reviews number (MathSciNet)
MR3375883

Zentralblatt MATH identifier
1325.60117

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 93E15: Stochastic stability 65C50: Other computational problems in probability

Keywords
Second-order BSDEs weak approximation numerical scheme robustness of BSDE

Citation

Possamaï, Dylan; Tan, Xiaolu. Weak approximation of second-order BSDEs. Ann. Appl. Probab. 25 (2015), no. 5, 2535--2562. doi:10.1214/14-AAP1055. https://projecteuclid.org/euclid.aoap/1438261048


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