2 citations · 5 across the 11 of their papers we have counts for
13 papers
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…
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…
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…
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations
Julia Ackermann, Arnulf Jentzen, Benno Kuckuck +1
It is a challenging topic in applied mathematics to solve high-dimensional nonlinear partial differential equations (PDEs). Standard approximation methods for nonlinear PDEs suffer…
Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems
Julia Ackermann, Matthias Ehrhardt, Thomas Kruse +1
This study revisits a recently proposed symmetric port-Hamiltonian single-file model in one dimension. The uniform streaming solutions are stable in the deterministic model. Howeve…
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…
Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems
Julia Ackermann, Thomas Kruse, Mikhail Urusov
We start with a stochastic control problem where the control process is of finite variation (possibly with jumps) and acts as integrator both in the state dynamics and in the targe…
Self-exciting price impact via negative resilience in stochastic order books
Julia Ackermann, Thomas Kruse, Mikhail Urusov
Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation…
Inhomogeneous affine Volterra processes
Julia Ackermann, Thomas Kruse, Ludger Overbeck
We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions of Volterra equations driven by a Brownian motion with an…
Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models
Julia Ackermann, Thomas Kruse, Mikhail Urusov
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in continuous time. Both order book de…
Optimal trade execution in an order book model with stochastic liquidity parameters
Julia Ackermann, Thomas Kruse, Mikhail Urusov
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and res…