About me: My name is Stephan Eckstein and since January 2024 I am a junior professor in the math department at the University of Tübingen and also a member of the University's machine learning cluster. Most of my work is at the intersection of probability theory and machine learning, and related to stochastic optimization and numerical approximation. Specific topics I study currently are in the areas of optimal transport, regularization, causality, graphical probabilistic structures and (graph) neural networks.
Contact: Firstname.Lastname@uni-tuebingen.de (where Firstname=Stephan, Lastname=Eckstein).
Publications:
Optimal nonparametric estimation of the expected shortfall risk. Preprint. 2024. (joint work with Daniel Bartl)
Estimating the Rate-Distortion Function by Wasserstein Gradient Descent. ICML workshop and NeurIPS. 2023. (joint work with Stephan Mandt, Marcel Nutz and Yibo Yang)
Optimal transport and Wasserstein distances for causal models. Preprint. 2023. (joint work with Patrick Cheridito)
Stability and Sample Complexity of Divergence Regularized Optimal Transport. Preprint. 2022. (joint work with Erhan Bayraktar and Xin Zhang)
Convergence Rates for Regularized Optimal Transport via Quantization. Forthcoming in Mathematics of Operations Research. 2022. (joint work with Marcel Nutz)
Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithm. Forthcoming in SIAM Journal on Mathematical Analysis. 2022+. (joint work with Marcel Nutz)
Dimensionality Reduction and Wasserstein Stability for Kernel Regression. Preprint. 2022. (joint work with Armin Iske and Mathias Trabs)
Computational methods for adapted optimal transport. Forthcoming in Annals of Applied Probability. 2022. (joint work with Gudmund Pammer)
Limits of random walks with distributionally robust transition probabilities. Electronic Communications in Probability. 2021. (joint work with Daniel Bartl and Michael Kupper)
Robust pricing and hedging of options on multiple assets and its numerics. SIAM Journal on Financial Mathematics. 2021. (joint work with Gaoyue Guo, Tongseok Lim and Jan Obloj)
Minmax methods for optimal transport and beyond: regularization, approximation and numerics. NeurIPS. 2020. (joint work with Luca De Gennaro Aquino)
Martingale transport with homogeneous stock movements. Quantitative Finance, 1-10. 2020. (joint work with Michael Kupper)
Robust risk aggregation with neural networks. Mathematical Finance, 30(4), 1229-1272. 2020. (joint work with Michael Kupper and Mathias Pohl)
Computation of optimal transport and related hedging problems via penalization and neural networks. Applied Mathematics & Optimization, 83, 639–667. 2021. (joint work with Michael Kupper)
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