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Title: Qualitative robustness of set-valued value-at-risk Authors:  Elisa Mastrogiacomo - Insubria University (Italy) [presenting]
Giovanni Crespi - LIUC (Italy)
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 misspecification errors, as well as estimation errors on the final conclusion. 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.