• Corpus ID: 245836917

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

@inproceedings{Wang2022SmoothNS,
  title={Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions},
  author={Wenjia Wang and Yanyuan Wang and Xiaowei Zhang},
  year={2022}
}
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… 

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References

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A decomposition technique for portfolio risk measurement is proposed, through which a high-dimensional problem may be decomposed into low-dimensional ones that allow an efficient use of the kernel smoothing approach.

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TLDR
The asymptotically optimal rates of convergence for different estimators are presented and central limit theorems are established for some of the estimators proposed, which have major potential application areas including calculation of Value at Risk (VaR) in the field of mathematical finance and Bayesian performance analysis.
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