Neural optimal stopping boundary

Andres Max Reppen; Halil Mete Soner; Valentin Tissot-Daguette

doi:10.1111/mafi.12450

Neural optimal stopping boundary

Andres Max Reppen, Halil Mete Soner, Valentin Tissot-Daguette

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

Original language	English (US)
Pages (from-to)	441-469
Number of pages	29
Journal	Mathematical Finance
Volume	35
Issue number	2
DOIs	https://doi.org/10.1111/mafi.12450
State	Published - Apr 2025

All Science Journal Classification (ASJC) codes

Accounting
Finance
Social Sciences (miscellaneous)
Economics and Econometrics
Applied Mathematics

Keywords

American derivatives
Bermudan options
deep learning
fuzzy boundary
optimal stopping
stopping boundary problems

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10.1111/mafi.12450

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AB - A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

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KW - Bermudan options

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KW - fuzzy boundary

KW - optimal stopping

KW - stopping boundary problems

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Neural optimal stopping boundary

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All Science Journal Classification (ASJC) codes

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