Preprints
- Neural stochastic Volterra equations: learning path-dependent dynamics,
with David Scheffels, arXiv:2407.19557, 2024. - Functional differential equations driven by càdlàg rough paths,
with Anna P. Kwossek and Andreas Neuenkirch, arxiv:2403.17573, 2024. - Characterization of Besov spaces with dominating mixed smoothness by differences,
with Paul Nikolaev and Mathias Trabs, arXiv:2403.04469, 2024. - Quantitative relative entropy estimates on the whole space for convolution interaction forces,
with Paul Nikolaev, arXiv:2401.08938, 2024. - Pathwise convergence of the Euler scheme for rough and stochastic differential equations,
with Andrew L. Allan, Anna P. Kwossek and Chong Liu, arXiv:2309.16489, 2023. - Mean-field stochastic Volterra equations,
with David Scheffels, arXiv:2307.13775, 2023.
Papers
- Hegselmann-Krause model with environmental noise,
with Li Chen and Paul Nikolaev, to appear in Trans. Amer. Math. Soc., 2024+. - Pathwise uniqueness for singular stochastic Volterra equations with Hölder coefficients,
with David Scheffels, to appear in Stoch. PDE: Anal. Comp., 2024+. - Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations,
with Li Chen and Paul Nikolaev, Math. Methods Appl. Sci., vol. 47, no. 11, p. 9222--9248, 2024. - A Càdlàg Rough Path Foundation for Robust Finance,
with Andrew L. Allan and Chong Liu, Finance Stoch., vol. 28, no. 1, p. 215--257, 2024. - On the existence of weak solutions to stochastic Volterra equations,
with David Scheffels, Electron. Commun. Probab., vol. 28, no. 52, p. 1--12, 2023. - Model-free Portfolio Theory: A Rough Path Approach,
with Andrew L. Allan, Christa Cuchiero, Chong Liu, Math. Finance, vol. 33, no. 3, p. 709--765, 2023. - Stochastic Volterra equations with Hölder diffusion coefficients,
with David Scheffels, Stoch. Process. Appl., vol. 161, p. 291--315, 2023. - Optimal extension to Sobolev rough paths,
with Chong Liu and Josef Teichmann, Potential Anal. 59, vol. 59, p. 1399--1424, 2023. - A Sobolev rough path extension theorem via regularity structures,
with Chong Liu and Josef Teichmann, ESAIM Probab. Stat., vol. 27, p. 136--155, 2023. - One-dimensional game-theoretic differential equations,
with Rafał M. Łochowski and Nicolas Perkowski. Int. J. Approx. Reason., vol. 141, p. 11--27, 2022. - Càdlàg rough differential equations with reflecting barriers,
with Andrew L. Allan and Chong Liu, Stoch. Process. Appl., vol. 142, p. 79--104, 2021. - Paracontrolled distribution approach to stochastic Volterra equations,
with Mathias Trabs, J. Differential Equations, vol. 302, p. 222--272, 2021. - Local times and Tanaka-Meyer formulae for cadlag paths,
with Rafał Łochowski, Jan Obłój, and Pietro Siorpaes, Electron. J. Probab., vol. 26, no. 77, p. 1--29, 2021. - Martingale Optimal Transport Duality,
with Patrick Cheridito, Matti Kiiski and H. Mete Soner, Math. Ann., vol. 379, no. 3–4, p. 1685--1712 , 2021. - Stochastic Analysis with Modelled Distributions,
with Chong Liu and Josef Teichmann, Stoch. PDE: Anal. Comp., vol. 9, no. 2, p. 343--379, 2021. - On Sobolev rough paths,
with Chong Liu and Josef Teichmann, J. Math. Anal. Appl., vol. 497, no. 1, 124876, 2021. - Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker-Planck equations,
with Leif Döring, Lukas Gonon and Oleg Reichmann, J. Theoret. Probab. 34, no. 1, p. 173–205, 2021. - Characterization of non-linear Besov spaces,
with Chong Liu and Josef Teichmann, Trans. Amer. Math. Soc., vol. 373, no. 1, p. 529–550, 2020. - On Skorokhod Embeddings and Poisson Equations,
with Leif Döring, Lukas Gonon and Oleg Reichmann, Ann. Appl. Probab., vol. 29, no. 4, p. 2302-2337, 2019. - Duality for pathwise superhedging in continuous time,
with Daniel Bartl, Michael Kupper and Ludovic Tangpi, Finance Stoch., vol. 23, no. 3, p. 697–728, 2019. - A superhedging approach to stochastic integration,
with Rafał M. Łochowski and Nicolas Perkowski, Stoch. Process. Appl., vol. 128, no. 12, p. 4078–4103, 2018. - Rough path metrics on a Besov-Nikolskii type scale,
with Peter K. Friz, Trans. Amer. Math. Soc., vol. 370, no. 12, p. 8521-8550, 2018. - Examples of Itô càdlàg rough paths,
with Chong Liu, Proc. Amer. Math. Soc., vol. 146, no. 11, p. 4937-4950, 2018. - Pathwise super-replication via Vovk's outer measure,
with Mathias Beiglböck, Alexander M. G. Cox, Martin Huesmann and Nicolas Perkowski, Finance Stoch., vol. 21, no. 4, p. 1141-1166, 2017. - Rough differential equations driven by signals in Besov spaces,
with Mathias Trabs, J. Differential Equations, vol. 260, no. 6, p. 5202-5249, 2016. - Pathwise stochastic integrals for model free finance,
with Nicolas Perkowski, Bernoulli, vol. 22, no. 4, p. 2486-2520, 2016. - Existence of Levy's area and pathwise integration,
with Peter Imkeller, Commun. Stoch. Anal., vol. 9, no. 1, p. 93–111, 2015. - An FBSDE approach to the Skorokhod embedding problem for Gaussian processes with non-linear drift,
with Alexander Fromm and Peter Imkeller, Electron. J. Probab., vol. 20, no. 127, 1–38, 2015. - Local times for typical price paths and pathwise Tanaka formulas,
with Nicolas Perkowski, Electron. J. Probab., vol. 20, no. 46, p. 1–15, 2015.