Convergence rates for Backward SDEs driven by L\'evy processes

We consider L\'evy processes that are approximated by compound Poisson processes and, correspondingly, BSDEs driven by L\'evy 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 t...

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Bibliographic Details
Main Authors Liu, Chenguang, Papapantoleon, Antonis, Saplaouras, Alexandros
Format Journal Article
LanguageEnglish
Published 02.02.2024
Subjects
Mathematics - Optimization and Control
Mathematics - Probability
Quantitative Finance - Mathematical Finance
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Summary:We consider L\'evy processes that are approximated by compound Poisson processes and, correspondingly, BSDEs driven by L\'evy 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 L\'evy processes. The rate of convergence of the L\'evy processes depends on the Blumenthal--Getoor index of the process. We derive the rate of convergence for the BSDEs in the $\mathbb L^2$-norm and in the Wasserstein distance, and show that, in both cases, this equals the rate of convergence of the corresponding L\'evy process, and thus is optimal.
DOI:10.48550/arxiv.2402.01337