R: Conditional Tail Expectation

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 [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.

### 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:

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.

### 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

`aggregateDist`; `VaR`

### 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)

[Package actuar version 3.1-2 Index]