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：括号模拟涉及通过模拟估计有条件期望的功能。 在本文中,我们提出了基于内核脊回归的新方法,以利用有条件期望的顺畅性作为多功能调节变量的函数。 Asympt分析表明,随着模拟预算的增加,拟议的方法可以有效减轻对合并率的维度诅咒,条件是有条件期望足够平稳。 平滑弥合了立方根汇合率(即标准嵌套模拟的最佳率)和平方根汇合率(即标准蒙特卡洛模拟的金字塔率)之间的差距。 我们通过组合风险管理和投入不确定性量化的数字实例,展示了拟议方法的绩效。