Thomas Kruse
Photo by rolf-wegst.de
About me
Welcome to my homepage!
I am professor for uncertainty quantification and risk analysis at the Department of Mathematics and Informatics of the University of Wuppertal. You find my homepage at the University of Wuppertal here.
Prior to coming to Wuppertal I was professor at the Institute of Mathematics of the Justus Liebig University Giessen.
I held postdoctoral positions in the research group Applied Stochastics at the University of Duisburg-Essen, in the research group Stochastic Analysis at the University of Duisburg-Essen and at the Laboratoire de Mathématiques et Modélisation d'Évry.
I completed my Ph.D. studies at the University of Bonn where I was a member of the Bonn International Graduate School in Mathematics.
Contact
University of Wuppertal
Department of Mathematics and Informatics
Gaußstraße 20
42119 Wuppertal
Germany
Room: G.14.23
Phone: +49 202 439-5239
Email: tkruse (at) uni-wuppertal.de
Submitted Articles
See also Google Scholar for an overview of my research articles.
Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems, with J. Ackermann and M. Urusov, 2022 [arXiv]
On effects of negative resilience on optimal trade execution in stochastic order books, with J. Ackermann and M. Urusov, 2021. [arXiv]
Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations, with C. Beck and A. Jentzen, 2020. [arXiv]
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities, with M. Hutzenthaler, A. Jentzen and T. Nguyen, 2022. [arXiv]
Optimal Control of an Epidemic through Social Distancing, with P. Strack, Cowles Foundation Discussion Paper No. 2229, 2020. [SSRN]
Publications
On the speed of convergence of Picard iterations of backward stochastic differential equations, with M. Hutzenthaler and T. Nguyen, to appear in Probability, Uncertainty and Quantitative Risk, 2022. [arXiv]
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations, with A. Jentzen, M. Hutzenthaler and T. Nguyen, to appear in Journal of Numerical Mathematics, 2022. [arXiv]
Inhomogeneous affine Volterra processes, with J. Ackermann and L. Overbeck, Stochastic Processes and their Applications, 150, 250-279, 2022. [arXiv]
Properties of the EMCEL scheme for approximating irregular diffusions, with S. Ankirchner, W. Löhr and M. Urusov, Journal of Mathematical Analysis and Applications 509 (1), 2022. [arXiv]
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations, with M. Hutzenthaler and T. Nguyen, Journal of Mathematical Analysis and Applications 507 (1), 125761, 2021. [arXiv]
Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models, with J. Ackermann and M. Urusov, Finance & Stochastics 25 (4), 757-810, 2021. [arXiv]
Optimal trade execution in an order book model with stochastic liquidity parameters, with J. Ackermann and M. Urusov, SIAM Journal on Financial Mathematics 12 (2), 788-822, 2021. [arXiv]
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities, with M. Hutzenthaler and A. Jentzen, to appear in Foundations of Computational Mathematics, 2021. [arXiv]
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations, with W. E, M. Hutzenthaler, A. Jentzen, Partial Differential Equations and Applications 2 (6), 1-31, 2021. [arXiv]
Wasserstein convergence rates for random bit approximations of continuous Markov processes, with S. Ankirchner and M. Urusov, Journal of Mathematical Analysis and Applications 493 (2), 124543, 2020. [arXiv]
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations, with M. Hutzenthaler, A. Jentzen, T. Nguyen, P. von Wurstemberger, Proceedings of the Royal Society A, 476 (2244), 20190630, 2020. [arXiv]
A Toolkit for Robust Risk Assessment using F-Divergences, with J. Schneider and N. Schweizer, to appear in Management Science, 2020. [SSRN]
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations , with C. Beck, F. Hornung, M. Hutzenthaler and A. Jentzen, Journal of Numerical Mathematics, 28 (4), 197-222, 2020. [arXiv]
A functional limit theorem for coin tossing Markov chains, with S. Ankirchner and M. Urusov, Annales de l'Institut Henri Poincaré (B) Probability and Statistics 56 (4) 2996-3019, 2020. [arXiv]
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations , with M. Hutzenthaler, A. Jentzen and T. Nguyen, SN Partial Differential Equations and Applications, 1:1-34, 2020. [arXiv]
Approximating absorption times of continuous Markov processes, with M. Urusov, Discrete and Continuous Dynamical Systems - Series B, 25(9):3631- 3650, 2020. [arXiv]
Multilevel Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities, with M. Hutzenthaler, SIAM Journal on Numerical Analysis, 58(2): 929-961. 2020. [arXiv]
Optimal position targeting via decoupling fields, with S. Ankirchner, A. Fromm and A. Popier, Annals of Applied Probability, 30(2): 644-672. 2020. [hal]
Stopping with expectation constraints: 3 points suffice, with S. Ankirchner, N. Kazi-Tani, and M. Klein, Electronic Journal of Probability, 24 (2019), paper no. 66, 2019. [hal]
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations, with W. E, M. Hutzenthaler, A. Jentzen, Journal of Scientific Computing, 79(3): 1534–1571, 2019. [arXiv]
The Joint Impact of F-Divergences and Reference Models on the Contents of Uncertainty Sets, with J. Schneider and N. Schweizer, Operations Research, 67(2): 428-435, 2019. [SSRN]
An inverse optimal stopping problem for diffusions, with P. Strack, Mathematics of Operations Research, 44(2): 423-439, 2019. [arXiv]
Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values, with D. Sezer and A. Popier, Stochastics and Dynamics, 19:02, 2019. [hal]
A verification theorem for optimal stopping problems with expectation constraints, with S. Ankirchner and M. Klein, Applied Mathematics and Optimization, 79:145, 2019. [hal]
WLLN for arrays of nonnegative random variables, with S. Ankirchner and M. Urusov, Statistics and Probability Letters, 122:73-78, 2017. pdf
A functional limit theorem for irregular SDEs, with S. Ankirchner and M. Urusov, Annales de l'Institut Henri Poincaré (B) Probability and Statistics, 53(3):1438-1457, 2017. [arXiv]
Numerical approximation of irregular SDEs via Skorokhod embeddings, with S. Ankirchner and M. Urusov, Journal of Mathematical Analysis and Applications, 440(2):692-715, 2016. [hal]
Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting, with A. Popier, Stochastic Processes and their Applications, 126(9):2554-2592, 2016. [arXiv]
BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration, with A. Popier, Stochastics, 88(4):491-539, 2016. [arXiv] Please note that in the case p<2 and if the driver depends on the integrand with respect to the Poisson measure there is a mistake in the proof of Proposition 8. This is corrected in the paper below:
Lp-solution for BSDEs with jumps in the case p<2. Corrections to the paper "BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration", with A. Popier, Stochastics, 89(8):1201-1227, 2017. [hal]
Optimal Stopping with Private Information, with P. Strack, Journal of Economic Theory, 159:702-727, 2015. [SSRN]
Optimal position targeting with stochastic linear-quadratic costs, with S. Ankirchner, Banach Center Publications, 104:9-24, 2015. [pdf]
BSDEs with singular terminal condition and control problems with a constraint, with S. Ankirchner and M. Jeanblanc, SIAM Journal on Control and Optimization, 52(2):893–913, 2014. [arXiv]
Optimal Trade Execution Under Price-Sensitive Risk Preferences, with S. Ankirchner, Quantitative Finance, 13(9):1395–1409, 2013. [SSRN]
Hedging Forward Positions: Basis Risk Versus Liquidity Costs, with S. Ankirchner and P. Kratz, SIAM Journal on Financial Mathematics, 4:1, 668-696, 2013. [SSRN]