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 $\varepsilon$ and so demonstrate that our quantum Monte Carlo algorithm does not suffer from the curse of dimensionality.

翻译：在本文中,我们提供了一种量子蒙特卡洛算法,用以解决高维黑色拼图PDE与高维选项定价的关联性。该选项的回报功能是一般性的,只需要连续的和零碎的折叠式(CPWA),它涵盖了金融中所使用的大部分相关补偿功能。我们为我们的算法提供了严格的错误分析和复杂分析。特别是,我们证明,我们的算法的计算复杂性在PDE的空间维度上是多维的,是多维的,是多维的,是多维的,是PDE的美元,是规定精确度的对等,是$\varepsilon,从而证明我们的蒙泰卡洛算法不会受到维度的诅咒。</s>