Maximum CVaR (max_cvar_risk)
Contents
Maximum CVaR. There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). M new CVaR functions are calculated (for every Loss scenario function). Maximum CVaR is calculated by taking Maximum over M CVaR functions.
Syntax
max_cvar_risk(α, matrix_1,matrix_2,...,matrix_M) |
short call |
max_cvar_risk_name(α, 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.
is a confidence level.
.
Mathematical Definition
Maximum CVaR function is calculated as follows
,
where:
is CVaR Risk for 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 an argument of Maximum CVaR function.
Remarks
Data for calculation of Maximum CVaR are represented by a set of matrices of scenarios which may be in pmatrix form.
Example
See also
Maximum, Maximum for Gain, Maximum Deviation, Maximum Deviation for Gain, Maximum CVaR for Gain, Maximum CVaR Deviation, Maximum CVaR Deviation for Gain, Maximum VaR , Maximum VaR for Gain, Maximum VaR Deviation, Maximum VaR Deviation for Gain