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.

翻译：嵌套模拟旨在通过模拟估计条件期望的泛函。本文提出一种基于核岭回归的新方法，利用条件期望作为多维条件变量函数的平滑性。渐近分析表明，在模拟预算增加的前提下，若条件期望具有足够平滑性，所提方法能有效缓解维度灾难对收敛速度的影响。这种平滑性弥合了三次方根收敛速度（即标准嵌套模拟的最优收敛速度）与平方根收敛速度（即标准蒙特卡洛模拟的典范收敛速度）之间的差距。我们通过来自投资组合风险管理和输入不确定性量化的数值算例展示了所提方法的性能。