Convergence rates for Backward SDEs driven by Lévy processes
arxiv(2024)
摘要
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. We are
interested in the rate of convergence of the approximate BSDEs to the ones
driven by the Lévy processes. 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 𝕃^2-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.
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