CVaR Max for Gain. There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Gain scenarios function is calculated by maximizing losses over -(Linear Loss) functions (over M functions for every scenario).  CVaR Max for Gain is calculated by taking CVaR of the Maximum Gain scenarios.

 

Syntax

 

Parameters

matrix_m        is a Matrix of Scenarios:

       

where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.

is a confidence level, .

Mathematical Definition

CVaR Max for Gain function is calculated as follows

,

where:

is CVaR Risk for Loss function,

M =  number of random Loss Functions (See section Loss and Gain Functions):

,

 = vector of random coefficients for m-th Loss Function;

 = j-th scenario of the random vector ,

is a random function with scenarios:

.

is an argument of function.

 

Remarks

Every Loss Function is defined by a separate matrix of scenarios and has an equal number of scenarios J.

Probability of scenario  is defined by the first matrix.

 

Example

 

See also

CVaR Max

CVaR,

CVaR Normal Independent, CVaR Normal Dependent,

CVaR Deviation, CVaR Deviation Normal Independent, CVaR Deviation Normal Dependent,

CVaR for Mixture of Normal Independent, CVaR Deviation for Mixture of Normal Independent

CVaR Max Deviation,

CVaR for Discrete Distribution as Function of Atom Probabilities, CVaR for Mixture of Normal Distributions as Function of Mixture Weights