期刊
SIAM JOURNAL ON FINANCIAL MATHEMATICS
卷 6, 期 1, 页码 748-775出版社
SIAM PUBLICATIONS
DOI: 10.1137/140980089
关键词
optimal stopping; regression Monte Carlo; dynamic trees; active learning; expected improvement
类别
资金
- NSF [ATD-1222262]
- Direct For Mathematical & Physical Scien [1222262] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1222262] Funding Source: National Science Foundation
We propose a new approach to solving optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff and 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 multidimensional Bermudan options.
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