Conditional tail expectations

(Oct 10, 2014)

In a recent posting I looked at the calculation of percentiles and quantiles, which underpin many calculations for ICA and Solvency II.  Simply put, an \(\alpha\)-quantile is the value which is not expected to be exceeded \(\alpha\times 100\)% of the time.  This value is denoted \(Q_{\alpha}\).  Mathematically, for a continuous random variable, \(X\), and a given probability level \(\alpha\) we have:

$$\Pr(X\leq Q_\alpha)=\alpha$$

Thus, ICA and Solvency II work is about 99.5%-quantiles or \(Q_{99.5\%}\). However, quantiles and percentiles are not universally used for determining regulatory capital.  In North America, for example, the conditional tail expectation (CTE) is widely used.  The CTE…

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Tags: conditional tail expectation, CTE, quantile, percentile, coherence, subadditivity

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