| CTE {actuar} | R Documentation |
Conditional Tail Expectation
Description
Conditional Tail Expectation, also called Tail Value-at-Risk.
TVaR is an alias for CTE.
Usage
CTE(x, ...)
## S3 method for class 'aggregateDist'
CTE(x, conf.level = c(0.9, 0.95, 0.99),
names = TRUE, ...)
TVaR(x, ...)
Arguments
x |
an R object. |
conf.level |
numeric vector of probabilities with values
in |
names |
logical; if true, the result has a |
... |
further arguments passed to or from other methods. |
Details
The Conditional Tail Expectation (or Tail Value-at-Risk) measures the
average of losses above the Value at Risk for some given confidence
level, that is E[X|X > \mathrm{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 explicit formula given in Castañer et al. (2013) is
\mu + \frac{\sigma}{(1 - \alpha) \sqrt{2 \pi}}
e^{-\mathrm{VaR}(X)^2/2}
\left( 1 + \frac{\gamma}{6} \mathrm{VaR}(X) \right),
where, as above, \mu is the mean, \sigma the standard
deviation, \alpha the confidence level and \gamma is
the skewness.
Value
A numeric vector, named if names is TRUE.
Author(s)
Vincent Goulet vincent.goulet@act.ulaval.ca and Tommy Ouellet
References
Castañer, A. and Claramunt, M.M. and Mármol, M. (2013), Tail value at risk. An analysis with the Normal-Power approximation. In Statistical and Soft Computing Approaches in Insurance Problems, pp. 87-112. Nova Science Publishers, 2013. ISBN 978-1-62618-506-7.
See Also
Examples
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)