Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its proof of overcoming the curse of dimensionality
Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its proof of overcoming the curse of dimensionality
复制标题
求解金融高维期权定价 Black-Scholes PDE 的量子蒙特卡罗算法及其克服维数诅咒的证明
DOI：
10.48550/arxiv.2301.09241
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Ariel Neufeld
中科院分区：
文献类型：
--
作者：
Yongming Li;Ariel Neufeld
在本文中，我们提供了一个量子Monte Carlo算法来解决高维期权定价的相关性的高维Black-Scholes偏微分方程。购股权的支付功能为一般形式，仅须为连续及分段支付功能（CPWA），涵盖融资中使用的大部分相关支付功能。我们提供了一个严格的错误分析和我们的算法的复杂性分析。特别地，我们证明了该算法的计算复杂度在PDE的空间维数d和预定精度ε的倒数上是多项式有界的，从而证明了我们的量子Monte Carlo算法不受维数灾难的影响.
In this paper we provide a quantum Monte Carlo algorithm to solve high-dimensional Black-Scholes PDEs with correlation for high-dimensional option pricing. The payoff function of the option is of general form and is only required to be continuous and piece-wise affine (CPWA), which covers most of the relevant payoff functions used in finance. We provide a rigorous error analysis and complexity analysis of our algorithm. In particular, we prove that the computational complexity of our algorithm is bounded polynomially in the space dimension d of the PDE and the reciprocal of the prescribed accuracy ε and so demonstrate that our quantum Monte Carlo algorithm does not suffer from the curse of dimensionality.
影响因子：
6.4
作者：
Childs, Andrew M.;Liu, Jin-Peng;Ostrander, Aaron
通讯作者：
Ostrander, Aaron