Solving highdimensional optimal stopping problems using optimization based model order reduction
Abstract
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from the curse of dimensionality. Therefore, the objective of this paper is to establish dimension reduction schemes for largescale asset price models and to solve related optimal stopping problems (e.g. Bermudan option pricing) in the reduced setting, where regression is feasible. The proposed algorithm is based on an error measure between linear stochastic differential equations. We establish optimality conditions for this error measure with respect to the reduce system coefficients and propose a particular method that satisfies these conditions up to a small deviation. We illustrate the benefit of our approach in several numerical experiments, in which Bermudan option prices are determined.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.08951
 Bibcode:
 2022arXiv220508951R
 Keywords:

 Mathematics  Probability;
 60G40;
 60G51;
 65C30;
 91G60