RiskMeasure {AoE}R Documentation

Risk Measure

Description

Computes a number of (tail-related) risk measures for a number of distributions.

Usage

RiskMeasure(dist, par, rm, a = 0, b = Inf, eta = 1, p = 1)

Arguments

dist A character string indicating the distribution. See Details below.
par A numeric vector containing the parameters of the distribution. Parameters of the distribution. See Details below.
rm A character string containing the parameter of the distribution.
a, b Lower and upper level of an excess-of-loss contract; will be ignored unless rm = "XL".
eta Shape parameter in proportional hazards transform; will be ignored unless rm = "PH".
p Tail probability in case of expected shortfall, tail quantile, or economic capital. Will be ignored unless rm takes one of the values "EC", "ES", or "TQ".

Details

The purpose of this function is primarily to investigate the performance of various estimators of tail-related risk measures implemented by providing the true values for a number of heavy-tailed distributions.

The arguments dist and par determine for which distribution the desired risk measure will be computed:

"abs_t"
Distribution of the absolute value of a Student-t random variable with degrees of freedom nu determined by par.
"Pareto"
The Pareto distribution with shape parameter alpha determined by par.

The risk measure to be computed is determined by the value of the argument rm and, if relevant, the values of the arguments a, b, nu, and p:

"E"
Expectation E(X).
"EC"
Economic Capital, defined as Q(1-p) - E(X), with tail probability p.
"ES"
Expected Shortfall, defined as E[X | X>u], the threshold u = Q(1-p) being determined by the tail probability p.
"PH"
Proportional Hazards transform, defined as int_0^Inf (P(X > x))^eta dx with shape parameter eta.
"TQ"
Tail Quantile Q(1-p) with tail probability p.
"Var"
Variance var(X).
"XL"
Excess-of-Loss net premium E[max(min(X,b) - a)] with lower limit a and upper limit b. Set b = Inf in case of no upper limit.

Value

A number.

See Also

EconomicCapital, ExcessLoss, Expectation, ExpectedShortfall, PHtransform, Variance

Examples

# absolute values of random numbers from the t-distribution:
X <- abs(rt(n = 1000, df = 2))
# estimated tail quantile
TailQuantile(X, p = 0.001, k = (1:20)*5)
# true tail quantile
RiskMeasure(dist = "abs_t", par = 2, rm = "TQ", p = 0.001)

[Package AoE version 1.0.1 Index]