Risk Quantification in Stochastic Simulation under Input Uncertainty

TL;DR

This paper introduces risk measures for the mean response in stochastic simulations with input uncertainty, proposes a nested Monte Carlo method for estimation, and analyzes its statistical properties and efficient allocation strategies.

Contribution

It systematically studies risk quantification of mean response under input uncertainty, introducing new measures and estimation techniques with theoretical guarantees.

Findings

Proposed a nested Monte Carlo approach for risk estimation.

Established consistency and asymptotic normality of estimators.

Illustrated the importance of risk control in a sharing economy example.

Abstract

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.