输入不确定条件下随机模拟中的风险量化
Risk Quantification in Stochastic Simulation under Input Uncertainty
摘要：
在模拟复杂随机系统时，输出响应的行为依赖于从有限的真实世界数据中估计的输入参数，数据的有限性给系统带来了输入的不确定性。输入不确定性对输出响应的影响的量化已经得到了广泛的研究。现有的文献大多侧重于提供真实但未知输入参数下的平均响应的推断，包括点估计和置信区间构造。输入不确定性下的平均响应风险量化在系统评价和控制中起着重要的作用，因为它提供了对所有可能输入模型中平均响应极端情景的推断。据我们所知，在文献中很少有系统的研究。本文首先介绍了输入不确定性下均值响应的风险度量，并提出了一种嵌套的蒙特卡罗模拟方法来估计它们。然后，我们开发的渐近性质，如一致性和渐近正态性的建议嵌套风险估计。我们进一步研究了相关的预算分配问题，以有效的嵌套风险模拟，最后使用共享经济的例子来说明由于输入的不确定性，访问和控制风险的重要性。
英文摘要：
When simulating a complex stochastic system, the behavior of output response depends on input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty into the system. The quantification of the impact of input uncertainty on output response has been extensively studied. Most of the existing literature focuses on providing inferences on the mean response at the true but unknown input parameter, including point estimation and confidence interval construction. Risk quantification of mean response under input uncertainty often plays an important role in system evaluation and control, because it provides inferences on extreme scenarios of mean response in all possible input models. To the best of our knowledge, it has rarely been systematically studied in the literature. In this paper, first we introduce risk measures of mean response under input uncertainty, and propose a nested Monte Carlo simulation approach to estimate them. Then we develop asymptotical properties such as consistency and asymptotic normality for the proposed nested risk estimators. We further study the associated budget allocation problem for efficient nested risk simulation, and finally use a sharing economy example to illustrate the importance of accessing and controlling risk due to input uncertainty.
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