The Conditional Tail Expectation measures the average of losses above
the Value at Risk for some given confidence level, that is $E[X|X
> VaR(X)]$ where $X$ is the loss random variable. CTE is a generic function with, currently, only a method for
objects of class "aggregateDist".
For the recursive, convolution and simulation methods of
aggregateDist, the CTE is computed from the definition
using the empirical cdf.
For the normal approximation method, an explicit formula exists:
$$\mu + \frac{\sigma}{(1 - \alpha)} \sqrt{2 \pi}
e^{-\mathrm{VaR(X)}^2/2},$$
where $\mu$ is the mean, $\sigma$ the standard
deviation and $\alpha$ the confidence level.
For the Normal Power approximation, the CTE is computed from the
definition using integrate.