2012/04/11 by Volker Krätschmer, Krätschmer, Volker, Alexander Schied +3 · 4 citations
Decision Sciences · Economics, Econometrics and Finance · #28A33 #60B10 #60F05 #62G05 #62G35 #91B30 #Credit Risk and Financial Regulations #FOS: Economics and business #FOS: Mathematics #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1204.2458
openalex publication_date 2012/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel's classical notion of qualitative robustness is not suitable for risk measurement and we propose and analyze a refined notion of robustness that applies to tail-dependent law-invariant convex risk measures on Orlicz space. This concept of robustness captures the tradeoff between robustness and sensitivity and can be quantified by an index of qualitative robustness. By means of this index, we can compare various risk measures, such as distortion risk measures, in regard to their degree of robustness. Our analysis also yields results that are of independent interest such as continuity properties and consistency of estimators for risk measures, or a Skorohod representation theorem for ψ-weak convergence.