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Qualitative robustness of set-valued value-at-risk

Giovanni Paolo Crespi () and Elisa Mastrogiacomo ()
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Giovanni Paolo Crespi: Universitá degli Studi dell’Insubria
Elisa Mastrogiacomo: Universitá degli Studi dell’Insubria

Mathematical Methods of Operations Research, 2020, vol. 91, issue 1, No 3, 25-54

Abstract: Abstract Risk measures are defined as functionals of the portfolio loss distribution, thus implicitly assuming the knowledge of such a distribution. However, in practical applications, the need for estimation arises and with it the need to study the effects of mis-specification errors, as well as estimation errors on the final conclusion. In this paper we focus on the qualitative robustness of a sequence of estimators for set-valued risk measures. These properties are studied in detail for two well-known examples of set-valued risk measures: the value-at-risk and the maximum average value-at-risk. Our results illustrate, in particular, that estimation of set-valued value-at-risk can be given in terms of random sets. Moreover, we observe that historical set-valued value-at-risk, while failing to be sub-additive, leads to a more robust procedure than alternatives such as the maximum likelihood average value at-risk.

Keywords: Set-optimization; Set-valued risk-measure; Robustness; Set-valued value-at-risk (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-020-00707-9

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Handle: RePEc:spr:mathme:v:91:y:2020:i:1:d:10.1007_s00186-020-00707-9