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：嵌套模拟涉及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，当模拟预算增加时，若条件期望足够平滑，所提方法能有效缓解收敛率上的维度灾难。平滑性弥合了立方根收敛率（即标准嵌套模拟的最优速率）与平方根收敛率（即标准蒙特卡洛模拟的典型速率）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中的数值示例展示了所提方法的性能。