Quantum Algorithm for Stochastic Optimal Stopping Problems
Friday April 8, 2022 • 2:00 PM
João Doriguello joined us from the National University of Singapore to share his least squares Monte Carolo algorithm.
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 Monte Carlo techniques. For this algorithm we elucidate the intricate interplay of function approximation and quantum Monte Carlo algorithms. 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.
For more information, contact:
Chelsea Donahue, Rethinc. Labs Assistant Director
Chelsea_Donahue@kenan-flagler.unc.edu
João Doriguello
National University of Singapore
João has recently finished his PhD at the University of Bristol under the supervision of Ashley Montanaro and is currently based at the National University of Singapore working with Miklos Santha. He is mainly interested in communication complexity, Boolean analysis, quantum algorithms and quantum finance.