Conditional Tail Expectation
Conditional Tail Expectation, also called Tail Value-at-Risk.
TVaR is an alias for CTE.
CTE(x, ...)
## S3 method for class 'aggregateDist'
CTE(x, conf.level = c(0.9, 0.95, 0.99),
names = TRUE, ...)
TVaR(x, ...)x |
an R object. |
conf.level |
numeric vector of probabilities with values in [0, 1) |
.
names |
logical; if true, the result has a |
... |
further arguments passed to or from other methods. |
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:
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 explicit formula given in Castañer et al. (2013) is
m + s exp(-VaR(X)^2/2)/((1 - a) * sqrt(2 pi)) (1 + g * VaR(X)/6),
where, as above, m is the mean, s the standard deviation, a the confidence level and g is the skewness.
A numeric vector, named if names is TRUE.
Vincent Goulet vincent.goulet@act.ulaval.ca and Tommy Ouellet
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.
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.