Average 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 for every scenario (over M functions for every scenario).  Average Max for Gain is calculated by averaging 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.

.

Mathematical Definition

Average Max for Gain function is calculated as follows

,

where:

is Average Loss function,

M =  number of random Loss Functions ,

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

 = j-th scenario of the random vector ,

is a random function with scenarios .

 

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.

 

is an argument of Average Max for Gain function.

 

Example

 

See also

Average Loss, Average Gain, Average Max, Average Max Deviations, Average Max Deviation for Gain