Weak approximation of second-order BSDEs

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.

Published at http://dx.doi.org/10.1214/14-AAP1055 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Cited by in corpus (4)

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• Stability results for martingale representations: the general case
• Duality and approximation of stochastic optimal control problems under expectation constraints
• Reflections on BSDEs