Quantum algorithm for stochastic optimal stopping problems with applications in finance
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.15332
 Bibcode:
 2021arXiv211115332D
 Keywords:

 Quantum Physics;
 Mathematics  Probability;
 Quantitative Finance  Computational Finance
 EPrint:
 45 pages