We show that the conservative estimate of the value-at-risk (VaR) for the sum of d random losses with given identical marginals and finite mean is equivalent to the corresponding conservative estimate of the expected shortfall in the limit, as the number of risks becomes arbitrarily large. Examples of interest in quantitative risk management show that the equivalence also holds for relatively small and inhomogeneous risk portfolios. When the individual random losses have infinite first moment, we show that VaR can be arbitrarily large with respect to the corresponding VaR estimate for comonotonic risks if the risk portfolio is large enough.

Asymptotic equivalence of conservative value-at-risk- and expected shortfall-based capital charges / G. Puccetti, L. Rüschendorf. - In: THE JOURNAL OF RISK. - ISSN 1465-1211. - 16:3(2014 Feb), pp. 3-22. [10.21314/jor.2014.291]

Asymptotic equivalence of conservative value-at-risk- and expected shortfall-based capital charges

G. Puccetti
Primo
;
2014

Abstract

We show that the conservative estimate of the value-at-risk (VaR) for the sum of d random losses with given identical marginals and finite mean is equivalent to the corresponding conservative estimate of the expected shortfall in the limit, as the number of risks becomes arbitrarily large. Examples of interest in quantitative risk management show that the equivalence also holds for relatively small and inhomogeneous risk portfolios. When the individual random losses have infinite first moment, we show that VaR can be arbitrarily large with respect to the corresponding VaR estimate for comonotonic risks if the risk portfolio is large enough.
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore SECS-S/01 - Statistica
Settore MAT/06 - Probabilita' e Statistica Matematica
feb-2014
http://doi.org/10.21314/JOR.2014.291
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/975128
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