Quantitative Statistical Robustness in Distributionally Robust Optimization Models

In distributionally robust optimization (DRO) models, sample data of the underlying exogenous uncertainty parameters are often used to construct an ambiguity set of plausible probability distributions. It is common to assume that the sample data do not contain noise. This assumption may not be fulfilled in some data-driven problems where the perceived data are potentially … Read more

Data-Driven Distributionally Preference Robust Optimization Models Based on Random Utility Representation in Multi-Attribute Decision Making

Preference robust optimization (PRO) has recently been studied to deal with utility based decision making problems under ambiguity in the characterization of the decision maker’s (DM) preference. In this paper, we propose a novel PRO modeling paradigm which combines the stochastic utility theory with distributionally robust optimization technique. Based on the stochastic utility theory, our … Read more

Utility Preference Robust Optimization with Moment-Type Information Structure

Utility preference robust optimization (PRO) models are recently proposed to deal with decision making problems where the decision maker’s true utility function is unknown and the optimal decision is based on the worst case utility function from an ambiguity set of utility functions. In this paper, we consider the case where the ambiguity set is … Read more

Statistical Robustness in Utility Preference Robust Optimization Models

Utility preference robust optimization (PRO) concerns decision making problems where information on decision maker’s utility preference is incomplete and has to be elicited through partial information and the optimal decision is based on the worst case utility function elicited. A key assumption in the PRO models is that the true probability distribution is either known … Read more

Robust Spectral Risk Optimization When Information on Risk Spectrum Is Incomplete

Spectral risk measure (SRM) is a weighted average of value at risk (VaR) where the weighting function (also known as risk spectrum or distortion function) characterizes the decision maker’s risk attitude. In this paper, we consider the case where the decision maker’s risk spectrum is ambiguous and introduce a robust SRM model based on the … Read more