Triangle Quantum Computing Seminar Series: Quantum Algorithm for Stochastic Optimal Stopping Problems

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.
--Co-sponsors: IBM Quantum Hub at NC State, and Rethinc.Labs - Frank H. Kenan Institute of Private Enterprise at UNC - Chapel Hill