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

• Activity Number: 587 - Risk Modeling
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): Meng Xu* and José Miguel Angulo Ibáñez
• Companies: Sichuan University and University of Granada
• Keywords: Convex risk measure; Preference; Sensitivity analysis; Ambiguity; \phi-divergence risk measure; (h,\phi)-divergence risk measure

Abstract

This paper introduces a new family of the convex divergence-based risk measure by specifying (h,\phi)-divergence, corresponding with the dual representation. We first discuss the sensitivity characteristics of the modified divergence risk measure w.r.t P&L and the prior probability in the penalty term, in view of the certainty equivalent and robust statistics. Secondly, we show the similar sensitivity of (h,\phi)-divergence risk measure w.r.t P&L and prove that it is bounded with the analytic risk measure. The numerical studies designed for Renyi- and Tsallis-divergence risk measure are also provided. This new family involves all the actual divergence risk measures and relates to the divergence preferences.