CTE {actuar} | R Documentation |
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)