Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance

被引：36

作者：

An, Dong ^{[1
]}

Linden, Noah ^{[2
]}

Liu, Jin-Peng ^{[3
,4
,5
]}

Montanaro, Ashley ^{[2
,6
]}

Shao, Changpeng ^{[2
]}

Wang, Jiasu ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Univ Bristol, Sch Math, Fry Bldg, Bristol BS8 1UG, Avon, England

[3] Univ Maryland, Joint Ctr Quantum Informat & Comp Sci, College Pk, MD 20742 USA

[4] Univ Maryland, Inst Adv Comp Studies, College Pk, MD 20742 USA

[5] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[6] Phasecraft Ltd, Quantum Technol Innovat Ctr, Bristol BS1 5DD, Avon, England

来源：

QUANTUM | 2021年 / 5卷

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.22331/q-2021-06-24-481

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic speed-up for multilevel Monte Carlo methods in a general setting. As applications, we apply it to compute expectation values determined by classical solutions of SDEs, with improved dependence on precision. We demonstrate the use of this algorithm in a variety of applications arising in mathematical finance, such as the Black-Scholes and Local Volatility models, and Greeks. We also provide a quantum algorithm based on sublinear binomial sampling for the binomial option pricing model with the same improvement.

引用

页数：37

共 61 条

[1] Variable time amplitude amplification and quantum algorithms for linear algebra problems [J].