论文标题
光滑的嵌套模拟：在高尺寸的情况下桥接立方和平方根的收敛速率
Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions
论文作者
论文摘要
嵌套模拟涉及通过仿真估计有条件期望的功能。在本文中，我们提出了一种基于内核脊回归的新方法，以利用条件期望的平稳性，这是多维条件变量的函数。渐近分析表明，提出的方法可以有效地减轻依赖性预算增加的汇率的诅咒，前提是条件期望足够平滑。平滑度桥接了立方根收敛速率（即标准嵌套模拟的最佳速率）和平方根收敛速率（即标准蒙特卡洛模拟的规范速率）之间的差距。我们通过投资组合风险管理和输入不确定性量化的数值示例来证明该方法的性能。
Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of the multidimensional conditioning variable. Asymptotic analysis shows that the proposed method can effectively alleviate the curse of dimensionality on the convergence rate as the simulation budget increases, provided that the conditional expectation is sufficiently smooth. The smoothness bridges the gap between the cubic root convergence rate (that is, the optimal rate for the standard nested simulation) and the square root convergence rate (that is, the canonical rate for the standard Monte Carlo simulation). We demonstrate the performance of the proposed method via numerical examples from portfolio risk management and input uncertainty quantification.
