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

1
School of Economics, Sichuan University, Chengdu 610065, China
2
Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(7), 634; https://doi.org/10.3390/e21070634
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)
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Abstract

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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