Average Max (avg_max_risk)
Contents
Average Max. There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Loss scenarios function is calculated by maximizing losses over Linear Loss functions (over M functions for every scenario). Average Max is calculated by averaging Maximum Loss scenarios.
Syntax
avg_max_risk(matrix_1,matrix_2,...,matrix_M) |
short call |
avg_max_risk_name(matrix_1,matrix_2,...,matrix_M) |
call with optional name |
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 function is calculated as follows
,
where:
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 function.
Example
Case Studies with Average Max
See also
Average Loss, Average Gain, Average Max for Gain, Average Max Deviations, Average Max Deviation for Gain