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4921数理金融中等数值题short

Infer Missing Tail Observation 6

题目

Sorted empirical losses are [1, 2, 3, 4, 7, 9, 12, x]. Using alpha=0.75, define empirical VaR as the ceil(alpha*n)-th order statistic and empirical ES as the average of losses at and beyond that cutoff. If empirical ES is 11.5, what is x?

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