Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions
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Convex risk measureSensitivity analysisf-divergence
Xu, M., & Angulo, J. M. (2019). Divergence-based risk measures: a discussion on sensitivities and extensions. Entropy, 21(7), 634.
SponsorshipThis research was funded by MINECO/FEDER, EU grant MTM2015-70840-P and MCIU/AEI/FEDER, UE grant PGC2018-098860-B-I00.
This paper introduces a new family of the convex divergence-based risk measure by specifying (h, f)-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, f)-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.