英文标题：
《Risk Quantification in Stochastic Simulation under Input Uncertainty》
---
作者：
Helin Zhu, Tianyi Liu and Enlu Zhou
---
最新提交年份：
2017
---
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.
---
中文摘要：
在模拟一个复杂的随机系统时，输出响应的行为取决于由有限的真实数据估计的输入参数，而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影响的量化已被广泛研究。现有文献大多侧重于对真实但未知输入参数下的平均响应进行推断，包括点估计和置信区间构造。输入不确定性下平均响应的风险量化通常在系统评估和控制中起着重要作用，因为它可以在所有可能的输入模型中对平均响应的极端情况进行推断。据我们所知，文献中很少对其进行系统研究。本文首先介绍了输入不确定性下平均响应的风险度量，并提出了一种嵌套蒙特卡罗模拟方法来估计它们。然后，我们发展了所提出的嵌套风险估计的渐近性质，如一致性和渐近正态性。我们进一步研究了有效嵌套风险模拟的相关预算分配问题，最后用一个共享经济的例子说明了由于输入不确定性而获取和控制风险的重要性。
---
分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
--
一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
--

---
PDF下载：
-->