Elicitable Risk Measures

Quant. Finance, Vol 15(5), 725-733, 2015 (doi 10.1080/14697688.2014.946955)

19 Pages Posted: 3 Oct 2013 Last revised: 12 May 2015

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Valeria Bignozzi

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Date Written: October 30, 2014

Abstract

A statistical functional is elicitable if it can be defined as the minimizer of a suitable expected scoring function (see Gneiting (2011), Ziegel (2013) and the references therein). With financial applications in view, we suggest a slightly more restrictive definition than Gneiting (2011), and we derive several necessary conditions. For monetary risk measures, we show that elicitability leads to a subclass of the shortfall risk measures introduced in Follmer and Schied (2002). In the coherent case, we show that the only elicitable risk measures are the expectiles. Further, we provide an alternative proof of the result in Ziegel (2013) that the only coherent comonotone elicitable risk measure is the expected loss.

Keywords: Elicitability, expectiles, shortfall risk measures, VaR, mixture continuity

Suggested Citation

Bellini, Fabio and Bignozzi, Valeria, Elicitable Risk Measures (October 30, 2014). Quant. Finance, Vol 15(5), 725-733, 2015 (doi 10.1080/14697688.2014.946955), Available at SSRN: https://ssrn.com/abstract=2334746 or http://dx.doi.org/10.2139/ssrn.2334746

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

Valeria Bignozzi (Contact Author)

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Via Bicocca degli Arcimboldi, 8
Milano, 20126
Italy

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
820
Abstract Views
2,954
rank
31,609
PlumX Metrics