Extremes for Coherent Risk Measures

21 Pages Posted: 2 Jul 2016 Last revised: 13 Mar 2017

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Jinzhu Li

Nankai University - School of Mathematical Sciences

Date Written: October 3, 2016

Abstract

Various concepts appeared in the existing literature to evaluate the risk exposure of a financial or insurance firm/subsidiary/line of business due to the occurrence of some extreme scenarios. Many of those concepts, such as Marginal Expected Shortfall or Tail Conditional Expectation, are simply some conditional expectations that evaluate the risk in adverse scenarios and are useful for signaling to a decision-maker the poor performance of its risk portfolio or to identify which sub-portfolio is likely to exhibit a massive downside risk. We investigate the latter risk under the assumption that it is measured via a coherent risk measure, which obviously generalizes the idea of only taking the expectation of the downside risk. Multiple examples are given and our numerical illustrations show how the asymptotic approximations can be used in the capital allocation exercise. We have concluded that the expectation of the downside risk does not fairly take into account the individual risk contribution when allocating the VaR-based regulatory capital, and thus, more conservative risk measurements are recommended. Finally, we have found that more conservative risk measurements do not improve the fairness of the cost of capital allocation when the uncertainty with parameter estimation is present, even at a very high level.

Keywords: Capital allocation, Coherent/Distortion risk measure, Conditional Tail Expectation, Extreme Value Theory, Marginal Expected Shortfall, Rapid Variation, Regular Variation.

JEL Classification: C44, D81

Suggested Citation

Asimit, Alexandru Vali and Li, Jinzhu, Extremes for Coherent Risk Measures (October 3, 2016). Insurance: Mathematics and Economics, Vol. 71, pp. 332-341.. Available at SSRN: https://ssrn.com/abstract=2803316 or http://dx.doi.org/10.2139/ssrn.2803316

Alexandru Vali Asimit (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Jinzhu Li

Nankai University - School of Mathematical Sciences ( email )

Weijin Road #94
Tianjin, 300071
China

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