Kavli Affiliate: Cheng Peng
| First 5 Authors: Anton Malandii, Siddhartha Gupte, Cheng Peng, Stan Uryasev,
| 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.
| Search Query: ArXiv Query: search_query=au:”Cheng Peng”&id_list=&start=0&max_results=10