most citedDeep 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

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math.OC2026

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…

math.OC2026

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…

math.OC2026

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…

math.OC2025

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…