We consider Lévy processes that are approximated by compound Poisson processes and, correspondingly, BSDEs driven by Lévy processes that are approximated by BSDEs driven by their compound Poisson approximations.
The rate of convergence of the Lévy processes depends on the Blumenthal — Getoor index of the process.
We derive the rate of convergence for the BSDEs in the L2-norm and in the Wasserstein distance, and show that, in both cases, this equals the rate of convergence of the corresponding Lévy process, and thus is optimal.
We introduce a comprehensive framework for analyzing convergence rates for infinite dimensional linear programming problems (LPs) within the context of the moment-sum-of-squares hierarchy.