Characterization and Construction of Sequentially Consistent Risk Measures

30 Pages Posted: 4 Oct 2013

See all articles by Valeria Bignozzi

Valeria Bignozzi

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Andreas Tsanakas

City University London - Cass Business School

Date Written: March 13, 2012

Abstract

In dynamic risk measurement the problem emerges of assessing the risk of a financial position at different times. Sufficient conditions are provided for conditional coherent risk measures, in order that the requirements of acceptance, rejection and sequential consistency are satisfied. It is shown that these conditions are often violated for standard methods of updating. A method is consequently proposed for constructing a sequentially consistent risk measure, which entails the modification of the set of probability measures used to obtain the risk assessment at an initial time. This is demonstrated for the coherent entropic risk measure and for the class of Choquet risk measures, which generalizes the well-known TVaR. Finally we consider the situation where the term of risk exposures is longer than the time horizon used in solvency assessment. Then, regulation such as Solvency II requires replacing the financial position itself with its fair value at the time horizon. We show that in this setting acceptance consistency can be preserved, though the same is not true about rejection consistency.

Keywords: dynamic risk measures, sequential consistency, TVaR, Choquet risk measure, coherent entropic risk measure

Suggested Citation

Bignozzi, Valeria and Tsanakas, Andreas, Characterization and Construction of Sequentially Consistent Risk Measures (March 13, 2012). Available at SSRN: https://ssrn.com/abstract=2335046 or http://dx.doi.org/10.2139/ssrn.2335046

Valeria Bignozzi (Contact Author)

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

Via Bicocca degli Arcimboldi, 8
Milano, 20126
Italy

Andreas Tsanakas

City University London - Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

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