Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
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DOI：
10.22331/q-2021-06-24-481
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发表时间：
2020-12
期刊：
影响因子：
6.4
通讯作者：
Dong An;N. Linden;Jin-Peng Liu;A. Montanaro;Changpeng Shao;Jiasu Wang
中科院分区：
文献类型：
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作者：
Dong An;N. Linden;Jin-Peng Liu;A. Montanaro;Changpeng Shao;Jiasu Wang
受常微分方程和偏微分方程量子算法最新进展的启发，我们研究随机微分方程（SDE）的量子算法。首先，我们提供了一种量子算法，可以在一般设置下为多级蒙特卡罗方法提供二次加速。作为应用，我们将其应用于计算由 SDE 的经典解确定的期望值，并提高了对精度的依赖性。我们演示了该算法在数学金融领域出现的各种应用中的使用，例如布莱克-斯科尔斯模型和局部波动率模型以及希腊模型。我们还为二项式期权定价模型提供了基于次线性二项式采样的量子算法，具有相同的改进。
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.