arxiv:2207.10838

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

Published on Jul 22, 2022

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Abstract

Variational quantum Monte Carlo combined with neural-network quantum states provides a novel approach to solving high-dimensional partial differential equations, demonstrated through multi-asset Black-Scholes pricing.

AI-generated summary

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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