Loss-Based Risk Measures

29 Pages Posted: 8 Oct 2011

See all articles by Rama Cont

Rama Cont

University of Oxford; CNRS

Romain Deguest

Fundvisory

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Date Written: February 1, 2011

Abstract

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the statistical robustness of estimators of loss-based risk measures: we provide a general criterion for qualitative robustness of risk estimators and compare this criterion with sensitivity analysis of estimators based on influence functions. Finally, we provide examples of statistically robust estimators for loss-based risk measures.

Keywords: risk measures, robustness, loss-based risk measures, quantile estimation

JEL Classification: C13, G10

Suggested Citation

Cont, Rama and Deguest, Romain and He, Xue Dong, Loss-Based Risk Measures (February 1, 2011). Available at SSRN: https://ssrn.com/abstract=1755291 or http://dx.doi.org/10.2139/ssrn.1755291

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

CNRS ( email )

LPSM
Sorbonne University
Paris
France

HOME PAGE: http://rama.cont.perso.math.cnrs.fr/

Romain Deguest

Fundvisory ( email )

112 rue la Boetie
Paris, 75008
France

HOME PAGE: http://www.fundvisory.com/

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

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