Conditional divergence risk measures

2022/11/08 by Giulio Principi, Principi, Giulio, Fabio Maccheroni +1
Decision Sciences · #91G70 #FOS: Economics and business #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2211.04592

openalex publication_date 2022/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures. In particular, we study the conditional counterpart of optimized certainty equivalents. In the process, we provide representation results for niveloids in the conditional L^∞-space. By employing such representation results we retrieve a conditional version of the variational formula for optimized certainty equivalents. In conclusion, we apply this formula to provide a variational representation of the conditional entropic risk measure.

Related

• Optimization of conditional convex risk measures
• On random convex analysis -- the analytic foundation of the module approach to conditional risk measures
• Formulation and properties of a divergence used to compare probability measures without absolute continuity and its application to uncertainty quantification
• Convex Risk Measures based on Divergence
• Conditional generalized quantiles based on expected utility model and equivalent characterization of properties