Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions

Wenjia Wang (), Yanyuan Wang () and Xiaowei Zhang ()
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Wenjia Wang: Data Science and Analytics Thrust, Information Hub, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511400, China
Yanyuan Wang: Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Special Administrative Region, China
Xiaowei Zhang: Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Special Administrative Region, China

Management Science, 2024, vol. 70, issue 12, 9031-9057

Abstract: 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.

Keywords: nested simulation; smoothness; kernel ridge regression; convergence rate (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:70:y:2024:i:12:p:9031-9057

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