What question did this study set out to answer?

This research aims to provide a comprehensive overview of the Risk Quadrangle and its applications in optimization.

June 3, 2026EURO Journal on Computational Optimization0 citationsOpen Access

The risk quadrangle in optimization: An overview with recent results and extensions

BGBogdan GrechukUniversity of Leicester AMAnton MalandiiBrown University RRR. T. RockafellarUniversity of Washington

Key Points

This research aims to provide a comprehensive overview of the Risk Quadrangle and its applications in optimization.
Survey of developments in the Risk Quadrangle since 2013.
Unification of various risk measures and their axioms.
Demonstrations in portfolio optimization, regression, and classification.
Introduced subregularity axioms that relax classical principles.
Linked statistical divergences to Risk Quadrangle duality, encompassing distributionally robust optimization (DRO).
Provided insights into application areas such as portfolio optimization and classification problems.

Abstract

• Unified survey of the Risk Quadrangle (since 2013). • Unifies risk, deviation, regret, error, and the shared statistic. • Subregularity axioms relax classical regularity and coherency. • Links statistical divergences to RQ duality, unifying DRO. • Demonstrations in portfolio optimization, regression, classification.

问 AI

Bookmark

View Full Paper