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.
Received: 13 June 2019 / Revised: 24 June 2019 / Accepted: 24 June 2019 / Published: 27 June 2019
PDF [871 KB, uploaded 27 June 2019]
This paper introduces a new family of the convex divergence-based risk measure by specifying
-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
-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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Xu, M.; Angulo, J.M. Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions. Entropy 2019, 21, 634.
Xu M, Angulo JM. Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions. Entropy. 2019; 21(7):634.
Xu, Meng; Angulo, José M. 2019. "Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions." Entropy 21, no. 7: 634.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.