Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing

2022/07/22 by Tianchen Zhao, Zhao, Tianchen, Chuhao Sun +7
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Numerical Analysis (math.NA) #Stochastic processes and financial applications #Stock Market Forecasting Methods

paper · pdf · doi:10.48550/arxiv.2207.10838

openalex publication_date 2022/07/22 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schrödinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.

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