Robust Value-at-Risk Optimization with Interval Random Uncertainty Set

This paper addresses a new uncertainty set - interval random uncertainty set for robust Value-at-Risk optimization. The form of interval random uncertainty set makes it suitable for capturing the downside and upside deviations of real-world data. These deviation measures capture distributional asymmetry and lead to better optimization results. We also apply our interval random chance-constrained programming to robust Value-at-Risk optimization under interval random uncertainty sets in the elements of mean vector. Numerical experiments with real market data indicate that our approach results in better portfolio performance.