Sequential Design for Optimal Stopping Problems
This work addresses computational efficiency in optimal stopping problems, particularly for pricing multi-dimensional Bermudan options, representing an incremental improvement over existing methods like Longstaff-Schwartz.
The authors tackled the problem of solving optimal stopping problems via simulation by introducing adaptive generation of stochastic grids that actively learn classifiers partitioning the state space into continuation and stopping regions, achieving an order of magnitude savings in design size in numerical experiments.
We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids anchoring the simulated sample paths of the underlying state process. This allows for active learning of the classifiers partitioning the state space into the continuation and stopping regions. To this end, we examine sequential design schemes that adaptively place new design points close to the stopping boundaries. We then discuss dynamic regression algorithms that can implement such recursive estimation and local refinement of the classifiers. The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of design size can be achieved. We also compare with existing benchmarks in the context of pricing multi-dimensional Bermudan options.