Leon Sallandt

TL;DR: This work treats infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an optimal feedback law, and uses low rank hierarchical tensor product approximation/tree-based tensor formats, in particular tensor trains (TT tensors), and multi-polynomials, together with high dimensional quadrature.

TL;DR: In this paper, the authors considered a stochastic optimal exit time feedback control problem, where the Bellman equation is solved approximatively via the policy iteration algorithm on a polynomial ansatz space by a sequence of linear equations.

TL;DR: In this paper, an efficient compression technique based on hierarchical tensors for popular option pricing methods is presented, which can be used for the computation of Bermudan option prices with the Monte Carlo least-squares approach as well as the dual martingale method, both using high-dimensional tensorized polynomial expansions.

TL;DR: In this article, the authors argue that tensor trains provide an appealing approximation framework for parabolic PDEs: the combination of reformulations in terms of backward stochastic differential equations and regression-type methods in the tensor format holds the promise of leveraging latent low-rank structures enabling both compression and efficient computation.

TL;DR: In this paper, the authors consider a finite horizon control system with associated Bellman equation and obtain a sequence of short time horizon problems, which they call local optimal control problems, and apply two different methods, one being the well-known policy iteration, where a fixed-point iteration is required for every time step.