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：嵌套模拟是通过仿真估计条件期望泛函的方法。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，当仿真预算增加时，若条件期望具有充分平滑性，所提方法能有效缓解收敛速率上的维度灾难。这种平滑性架起了立方根收敛速率（标准嵌套模拟的最优速率）与平方根收敛速率（标准蒙特卡洛仿真的典型速率）之间的桥梁。我们通过投资组合风险管理和输入不确定性量化领域的数值算例，验证了所提方法的性能。