论文标题
数学金融中的随机微分方程的量子加速多层次蒙特卡洛方法
Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
论文作者
论文摘要
受到普通和部分微分方程的量子算法的最新进展的启发，我们研究了随机微分方程（SDE）的量子算法。首先，我们提供了一种量子算法，该算法在一般环境中为多级蒙特卡洛方法提供了二次加速。作为应用程序，我们将其应用于计算由SDE的经典解决方案确定的期望值，并提高了对精度的依赖性。我们证明了该算法在数学金融中产生的各种应用中的使用，例如黑甲虫和局部波动率模型以及希腊人。我们还为二项式选项定价模型提供了基于均值二项式采样模型的量子算法，并提供了相同的改进。
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.
