Publications Prof. Dr. Thomas Kruse
- 2024
- T. Kruse and P. Strack, "Optimal dynamic control of an epidemic", Operations Research, vol. 72, no. 3, pp. 1031–1048, 2024. INFORMS.
- J. Ackermann, T. Kruse and M. Urusov, "Reducing Obizhaeva-Wang-type trade execution problems to LQ stochastic control problems", Finance and Stochastics, vol. 28, no. 3, pp. 813–863, 2024. Springer Verlag.
- J. Ackermann, T. Kruse and M. Urusov, "Self-exciting price impact via negative resilience in stochastic order books", Annals of Operations Research, vol. 336, no. 1, pp. 637–659, 2024. Springer Netherlands.
- J. Ackermann, M. Ehrhardt, T. Kruse and A. Tordeux, "Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems", Preprint, 2024.
- M. Ehrhardt, T. Kruse and A. Tordeux, "The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension", ESAIM: Mathematical Modelling and Numerical Analysis, vol. 58, no. 2, pp. 515–544, 2024. EDP Sciences.
- 2023
- J. Ackermann, A. Jentzen, T. Kruse, B. Kuckuck and J. L. Padgett, "Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the Lp-sense", Preprint, 2023.
- C. Beck, A. Jentzen, K. Kleinberg and T. Kruse, "Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems", Preprint, 2023.
- M. Hutzenthaler, A. Jentzen, T. Kruse and T. Anh Nguyen, "Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations", Journal of Numerical Mathematics, vol. 31, no. 1, pp. 1–28, 2023. De Gruyter.
- 2022
- J. Ackermann, T. Kruse and L. Overbeck, "Inhomogeneous affine Volterra processes", Stochastic Processes and their Applications, vol. 150, pp. 250–279, 2022. North-Holland.
- M. Hutzenthaler, T. Kruse and T. A. Nguyen, "Multilevel Picard approximations for McKean-Vlasov stochastic differential equations", Journal of Mathematical Analysis and Applications, vol. 507, no. 1, pp. 125761, 2022. Academic Press.
- M. Hutzenthaler, T. Kruse and T. A. Nguyen, "On the speed of convergence of Picard iterations of BSDEs", Probability, Uncertainty and Quantitative Risk, vol. 7, no. 2, 2022. American Institute of Mathematical Sciences.
- M. Hutzenthaler, A. Jentzen and T. Kruse, "Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities", Foundations of Computational Mathematics, vol. 22, no. 4, pp. 905–966, 2022. Springer New York.
- S. Ankirchner, T. Kruse, W. Löhr and M. Urusov, "Properties of the EMCEL scheme for approximating irregular diffusions", Journal of Mathematical Analysis and Applications, vol. 509, no. 1, pp. 125931, 2022. Academic Press.
- 2021
- J. Ackermann, T. Kruse and M. Urusov, "Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models", Finance and Stochastics, vol. 25, no. 4, pp. 757–810, 2021. Springer Verlag.
- M. Hutzenthaler, A. Jentzen, T. Kruse and others, "Multilevel Picard iterations for solving smooth semilinear parabolic heat equations", Partial Differential Equations and Applications, vol. 2, no. 6, pp. 1–31, 2021. Springer International Publishing.
- J. Ackermann, T. Kruse and M. Urusov, "Optimal trade execution in an order book model with stochastic liquidity parameters", SIAM Journal on Financial Mathematics, vol. 12, no. 2, pp. 788–822, 2021. Society for Industrial and Applied Mathematics.
- 2020
- S. Ankirchner, T. Kruse, M. Urusov and others, "A functional limit theorem for coin tossing Markov chains", Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol. 56, no. 4, pp. 2996–3019, 2020. Institute of Mathematical Statistics.
- M. Hutzenthaler, A. Jentzen, T. Kruse and T. A. Nguyen, "A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations", SN Partial Differential Equations and Applications, vol. 1, no. 2, pp. 1–34, 2020. Springer International Publishing.
- T. Kruse, J. Schneider and N. Schweizer, "A toolkit for robust risk assessment using F-divergences", Management Science, vol. 67, no. 10, 2020. INFORMS.
- T. Kruse and M. Urusov, "Approximating exit times of continuous Markov processes", Discrete and Continuous Dynamical Systems-B, vol. 25, no. 9, pp. 3631–3650, 2020. American Institute of Mathematical Sciences.
- M. Hutzenthaler, A. Jentzen, T. Kruse and T. A. Nguyen, "Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities", Preprint, 2020.
- M. Hutzenthaler and T. Kruse, "Multilevel Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities", SIAM Journal on Numerical Analysis, vol. 58, no. 2, pp. 929–961, 2020. Society for Industrial and Applied Mathematics.
- C. Beck, A. Jentzen and T. Kruse, "Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations", Preprint, 2020.
- S. Ankirchner, A. Fromm, T. Kruse and A. Popier, "Optimal position targeting via decoupling fields", The Annals of Applied Probability, vol. 30, no. 2, pp. 644–672, 2020. Institute of Mathematical Statistics.
- C. Beck, F. Hornung, M. Hutzenthaler, A. Jentzen and T. Kruse, "Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations", Journal of Numerical Mathematics, vol. 28, no. 4, pp. 197–222, 2020. De Gruyter.
