License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2022.2
URN: urn:nbn:de:0030-drops-165091
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16509/
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Doriguello, João F. ; Luongo, Alessandro ; Bao, Jinge ; Rebentrost, Patrick ; Santha, Miklos

Quantum Algorithm for Stochastic Optimal Stopping Problems with Applications in Finance

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LIPIcs-TQC-2022-2.pdf (0.9 MB)

Abstract

The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on quantum access to a stochastic process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo. For this algorithm, we elucidate the intricate interplay of function approximation and quantum algorithms for Monte Carlo. Our algorithm achieves a nearly quadratic speedup in the runtime compared to the LSM algorithm under some mild assumptions. Specifically, our quantum algorithm can be applied to American option pricing and we analyze a case study for the common situation of Brownian motion and geometric Brownian motion processes.

BibTeX - Entry

@InProceedings{doriguello_et_al:LIPIcs.TQC.2022.2,
  author =	{Doriguello, Jo\~{a}o F. and Luongo, Alessandro and Bao, Jinge and Rebentrost, Patrick and Santha, Miklos},
  title =	{{Quantum Algorithm for Stochastic Optimal Stopping Problems with Applications in Finance}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{2:1--2:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-237-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{232},
  editor =	{Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16509},
  URN =		{urn:nbn:de:0030-drops-165091},
  doi =		{10.4230/LIPIcs.TQC.2022.2},
  annote =	{Keywords: Quantum computation complexity, optimal stopping time, stochastic processes, American options, quantum finance}
}

Keywords: Quantum computation complexity, optimal stopping time, stochastic processes, American options, quantum finance
Collection: 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)
Issue Date: 2022
Date of publication: 04.07.2022

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