8 citations · 12 across the 6 of their papers we have counts for
6 papers
From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs
Lorenz Richter, Leon Sallandt, Nikolas Nüsken
The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called cur…
Approximating optimal feedback controllers of finite horizon control problems using hierarchical tensor formats
Mathias Oster, Leon Sallandt, Reinhold Schneider
Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associate…
Pricing high-dimensional Bermudan options with hierarchical tensor formats
Christian Bayer, Martin Eigel, Leon Sallandt +1
An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the "curse of dimensionality" can be alleviated f…
Solving high-dimensional parabolic PDEs using the tensor train format
Lorenz Richter, Leon Sallandt, Nikolas Nüsken
High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since tr…
Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format
Konstantin Fackeldey, Mathias Oster, Leon Sallandt +1
We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space…
Approximating the Stationary Bellman Equation by Hierarchical Tensor Products
Mathias Oster, Leon Sallandt, Reinhold Schneider
We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an opti…