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：本文提出了一种量子蒙特卡洛算法，用于求解具有相关性的高维Black-Scholes偏微分方程，以应用于高维期权定价。期权的收益函数为一般形式，仅需满足连续且分段仿射（CPWA）条件，这涵盖了金融领域所用的大多数相关收益函数。我们为算法提供了严格的误差分析和复杂度分析。特别地，我们证明了算法的计算复杂度在偏微分方程的空间维度$d$和规定精度$\varepsilon$的倒数上均为多项式有界，从而表明该量子蒙特卡洛算法不会遭受维度灾难。