CVaR for Gain Normal Dependent (cvar_risk_nd_g)
Contents
CVaR for Gain Normal Dependent. Special case of the CVaR for Gain when all coefficients in -(Linear Loss ) function are mutually dependent normally distributed random values
Syntax
cvar_risk_nd_g(α, matrix_mn,matrix_cov) |
short call |
cvar_risk_nd_g_name(α, matrix_mn,matrix_cov) |
call with optional name |
Parameters
matrix_mn is a PSG matrix of mean values:
where the header row contains names of variables. The second row contains numerical data.
matrix_cov is a PSG matrix of covariance values:
where the header row contains names of variables. Other rows contain numerical data.
is a confidence level.
Mathematical Definition
CVaR for Loss Normal Dependent function is calculated as follows:
,
where
is Loss Function (See section Loss and Gain Functions),
is a CVaR Risk for Loss Normal Dependent function,
,
,
,
is a probability density function of the standard normal distribution,
,
is the standard normal distribution,
is an argument of function.
Remarks
Matrix matrix_cov have to be symmetric.
Example
See also
CVaR,
CVaR Deviation, CVaR Deviation Normal Independent, CVaR Deviation Normal Dependent,
CVaR for Mixture of Normal Independent, CVaR Deviation for Mixture of Normal Independent
CVaR for Discrete Distribution as Function of Atom Probabilities, CVaR for Mixture of Normal Distributions as Function of Mixture Weights