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- W4382763292 abstract "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." @default.
- W4382763292 created "2023-07-01" @default.
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- W4382763292 date "2023-06-28" @default.
- W4382763292 modified "2023-10-17" @default.
- W4382763292 title "Divergence Based Quadrangle and Applications" @default.
- W4382763292 doi "https://doi.org/10.48550/arxiv.2306.16525" @default.
- W4382763292 hasPublicationYear "2023" @default.
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