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In this paper, an objective criterion, and a framework from which it was developed, are presented in order to decide whether or not a fitted distribution is inappropriate for the purpose of value-at-risk calculation. That criterion is based on established extreme value theory (principally the Pickands-Balkema-deHaan Theorem), which is used to calculate a sequence of reference value-at-risk estimates using Generalised Pareto distributions. Those estimates are used to develop a closed-form formula for calculating a theoretical \u2019maximum\u2019 value-at-risk. The method is validated by generating 100 random data sets and testing them against the framework for varying input parameter values. Approximately 75% of those cases passed the validation test.<\/jats:p>","DOI":"10.1007\/s11786-024-00579-w","type":"journal-article","created":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T07:03:35Z","timestamp":1716275015000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Credibility Framework for Extreme Value-at-Risk"],"prefix":"10.1007","volume":"18","author":[{"given":"Peter","family":"Mitic","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,21]]},"reference":[{"key":"579_CR1","doi-asserted-by":"publisher","DOI":"10.1214\/ao10.2307\/1968974p\/1176996548","author":"A Balkema","year":"1974","unstructured":"Balkema, A., Haan, L.: Residual life time at great age. Annals Probab. 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