Divergence Based Quadrangle and Applications

This paper introduces a novel framework for assessing risk and decision-making in the presence of uncertainty, the \emph{\(\varphi\)-Divergence Quadrangle}. This approach expands upon the traditional Risk Quadrangle, a model that quantifies uncertainty through four key components: \emph{risk, deviat...

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Bibliographic Details
Published inarXiv.org
Main Authors Malandii, Anton, Gupte, Siddhartha, Cheng, Peng, Uryasev, Stan
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.07.2023
Subjects
Decision making
Decision theory
Optimization
Risk assessment
Risk management
Statistical analysis
Uncertainty
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Summary:This paper introduces a novel framework for assessing risk and decision-making in the presence of uncertainty, the \emph{\(\varphi\)-Divergence Quadrangle}. This approach expands upon the traditional Risk Quadrangle, a model that quantifies uncertainty through four key components: \emph{risk, deviation, regret}, and \emph{error}. The \(\varphi\)-Divergence Quadrangle incorporates the \(\varphi\)-divergence as a measure of the difference between probability distributions, thereby providing a more nuanced understanding of risk. Importantly, the \(\varphi\)-Divergence Quadrangle is closely connected with the distributionally robust optimization based on the \(\varphi\)-divergence approach through the duality theory of convex functionals. To illustrate its practicality and versatility, several examples of the \(\varphi\)-Divergence Quadrangle are provided, including the Quantile Quadrangle. The final portion of the paper outlines a case study implementing regression with the Entropic Value-at-Risk Quadrangle. The proposed \(\varphi\)-Divergence Quadrangle presents a refined methodology for understanding and managing risk, contributing to the ongoing development of risk assessment and management strategies.
ISSN:2331-8422