Robust simulation of stochastic systems with input uncertainties modeled by statistical divergences

Simulation is often used to study stochastic systems. A key step of this approach is to specify a distribution for the random input. This is called input modeling, which is important and even critical for simulation study. However, specifying a distribution precisely is usually difficult and even impossible in practice. This issue is called input uncertainty in simulation study. In this paper we study input uncertainty when using simulation to estimate important performance measures: expectation, probability, and value-at-risk. We propose a robust simulation (RS) approach, which assumes the real distribution is contained in a certain ambiguity set constructed using statistical divergences, and simulates the maximum and the minimum of the performance measures when the distribution varies in the ambiguity set. We show that the RS approach is computationally tractable and the corresponding results can disclose important information about the systems, which may help decision makers better understand the systems.