MultiStatM (version 2.1.0)

MTCE: Multivariate tail conditional expectation

Description

It provides the conditional expectation $$ \text{MTCE}_q(\mathbf{X}) = \operatorname{E} \left( \mathbf{X} \mid X_1 > \text{VaR}_q (X_1), X_2 > \text{VaR}_q (X_2), \dots, X_n > \text{VaR}_q (X_d) \right),$$ for \(q \in (0,1)\), where \(\text{VaR}_q(X)\) is the q-th quantile of the random variable \(X\). Expectation is taken with respect to GramCharlier with the first 4 cumulants.

Usage

MTCE(X, cum)

Value

Numerator of the ratio

Denominator of the ratio

MTCE Conditional expected value

Arguments

X

a vector of unstandardized VaRq

cum

list of mean, variance, skewness and kurtosis vectors

Details

For further details see the references below,

References

Landsman, Z., Makov, U., & Shushi, T. (2016). Multivariate tail conditional expectation for elliptical distributions. Insurance: Mathematics and Economics, 70, 216-223.

See Also

Other Approximations: Edgeworth(), GramCharlier(), IntEdgeworth(), IntGramCharlier()

Examples

x <- c(2,3,4)
cum <- MomCumMVt(p = 12, d = 3, r = 4, nCum = TRUE)
CE <- MTCE(x, cum)