| CTE {actuar} | R Documentation |
Conditional Tail Expectation.
CTE(x, ...)
## S3 method for class 'aggregateDist':
CTE(x, conf.level = c(0.9, 0.95, 0.99),
names = TRUE, ...)
x |
an R object. |
conf.level |
numeric vector of probabilities with values in [0, 1) |
names |
logical; if true, the result has a names
attribute. Set to FALSE for speedup with many probs. |
... |
further arguments passed to or from other methods. |
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:
m + s exp(-VaR(X)^2/2)/((1 - a) * sqrt(2 pi)),
where m is the mean, s the standard deviation and a the confidence level.
For the Normal Power approximation, the CTE is computed from the
definition using integrate.
A numeric vector, named if names is TRUE.
Vincent Goulet vincent.goulet@act.ulaval.ca and Tommy Ouellet
model.freq <- expression(data = rpois(7))
model.sev <- expression(data = rnorm(9, 2))
Fs <- aggregateDist("simulation", model.freq, model.sev, nb.simul = 1000)
CTE(Fs)