Comparative and qualitative robustness for law-invariant risk measures

Volker Krätschmer (), Alexander Schied () and Henryk Zähle ()

Finance and Stochastics, 2014, vol. 18, issue 2, 295 pages

Abstract: 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 spaces. This concept 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 of independent interest such as continuity properties and consistency of estimators for risk measures, or a Skorohod representation theorem for ψ-weak convergence. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Law-invariant risk measure; Convex risk measure; Coherent risk measure; Orlicz space; Qualitative robustness; Comparative robustness; Index of qualitative robustness; Hampel’s theorem; ψ-Weak topology; Distortion risk measure; Skorohod representation; 62G35; 60B10; 60F05; 91B30; 28A33; D81 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (46)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00780-013-0225-4 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:18:y:2014:i:2:p:271-295

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-013-0225-4

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().