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Deep optimal stopping

by S. Becker and P. Cheridito and A. Jentzen

(Report number 2018-14)

Abstract
In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such it is broadly applicable in situations where the underlying randomness can efficiently be simulated. We test the approach on two benchmark problems: the pricing of a Bermudan max-call option on different underlying assets and the problem of optimally stopping a fractional Brownian motion. In both cases it produces very accurate results in high-dimensional situations with short computing times.

Keywords: optimal stopping, deep learning, Bermudan option, fractional Brownian motion

@Techreport{BCJ18_768,
  author = {S. Becker and P. Cheridito and A. Jentzen},
  title = {Deep optimal stopping},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-14.pdf },
  year = {2018}
}

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