6 papers
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 -sense
Julia Ackermann, Arnulf Jentzen, Thomas Kruse +2
Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have gener…
Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework
Julia Ackermann, Thomas Kruse, Mikhail Urusov
We analyze a continuous-time optimal trade execution problem in multiple assets where the price impact and the resilience can be matrix-valued stochastic processes that incorporate…
Time discretization of BSDEs with singular terminal condition using asymptotic expansion
Thomas Kruse, Julia Ackermann, Alexandre Popier
We consider a class of backward stochastic differential equations (BSDEs) with singular terminal condition and develop a numerical scheme to approximate their solution. To this end…
Matrix Riccati BSDEs with singular terminal condition and stochastic LQ control with linear terminal constraint
Julia Ackermann, Thomas Kruse, Petr Petrov +1
We analyze a class of multidimensional linear-quadratic stochastic control problems with random coefficients, motivated by multi-asset optimal trade execution. The problems feature…
Stochastic Passivity in Stochastic Differential Equations: A Port-Hamiltonian Perspective
Julia Ackermann, Thomas Kruse, Stefan Tappe
We extend deterministic port-Hamiltonian systems (PHS) to a stochastic framework by means of stochastic differential equations. As the dissipation inequality plays a crucial role f…
Modelling car-following dynamics with stochastic input-state-output port-Hamiltonian systems
Julia Ackermann, Matthias Ehrhardt, Thomas Kruse +1
In this contribution, we introduce a general class of car-following models with an input-state-output port-Hamiltonian structure. We derive stability conditions and long-term behav…