Deep neural network expressivity for optimal stopping problems

Lukas Gonon

Papers from arXiv.org

Abstract: This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces. A general framework is established in which the value function and continuation value of an optimal stopping problem can be approximated with error at most $\varepsilon$ by a deep ReLU neural network of size at most $\kappa d^{\mathfrak{q}} \varepsilon^{-\mathfrak{r}}$. The constants $\kappa,\mathfrak{q},\mathfrak{r} \geq 0$ do not depend on the dimension $d$ of the state space or the approximation accuracy $\varepsilon$. This proves that deep neural networks do not suffer from the curse of dimensionality when employed to solve optimal stopping problems. The framework covers, for example, exponential L\'evy models, discrete diffusion processes and their running minima and maxima. These results mathematically justify the use of deep neural networks for numerically solving optimal stopping problems and pricing American options in high dimensions.

Date: 2022-10
New Economics Papers: this item is included in nep-big, nep-cmp and nep-dcm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://arxiv.org/pdf/2210.10443 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2210.10443

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().