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Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions

School of Economics, Sichuan University, Chengdu 610065, China
Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain
Author to whom correspondence should be addressed.
Entropy 2019, 21(7), 634;
Received: 13 June 2019 / Revised: 24 June 2019 / Accepted: 24 June 2019 / Published: 27 June 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
PDF [871 KB, uploaded 27 June 2019]


This paper introduces a new family of the convex divergence-based risk measure by specifying ( h , ϕ ) -divergence, corresponding with the dual representation. First, the sensitivity characteristics of the modified divergence risk measure with respect to profit and loss (P&L) and the reference probability in the penalty term are discussed, in view of the certainty equivalent and robust statistics. Secondly, a similar sensitivity property of ( h , ϕ ) -divergence risk measure with respect to P&L is shown, and boundedness by the analytic risk measure is proved. Numerical studies designed for Rényi- and Tsallis-divergence risk measure are provided. This new family integrates a wide spectrum of divergence risk measures and relates to divergence preferences. View Full-Text
Keywords: convex risk measure; preference; sensitivity analysis; ambiguity; ϕ-divergence convex risk measure; preference; sensitivity analysis; ambiguity; ϕ-divergence

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Xu, M.; Angulo, J.M. Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions. Entropy 2019, 21, 634.

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