Weak approximation of second-order BSDEs
For researchers in stochastic control and numerical methods, this provides a theoretical foundation for approximating 2BSDEs, though the result is incremental as it extends existing BSDE approximation techniques.
The paper establishes a weak convergence result for second-order backward SDEs when continuous martingales are approximated by discrete ones, and provides concrete numerical schemes via controlled Markov chains, illustrated on examples.
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.