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Solving optimal stopping problems by backward induction in high dimensions isoften very complex since the computation of conditional expectations isrequired. Typically, such computations are based on regression, a method thatsuffers from the curse of dimensionality. Therefore, the objective of thispaper is to establish dimension reduction schemes for large-scale asset pricemodels and to solve related optimal stopping problems (e.g. Bermudan optionpricing) in the reduced setting, where regression is feasible. The proposedalgorithm is based on an error measure between linear stochastic differentialequations. We establish optimality conditions for this error measure withrespect to the reduce system coefficients and propose a particular method thatsatisfies these conditions up to a small deviation. We illustrate the benefitof our approach in several numerical experiments, in which Bermudan optionprices are determined.

Solving high-dimensional optimal stopping problems using optimization based model order reduction