Maximum VaR (max_var_risk)
Contents
Maximum VaR. There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). M new VaR functions are calculated (for every Loss scenario function). Maximum VaR is calculated by taking Maximum over M VaR functions.
Syntax
max_var_risk(α,matrix_1,matrix_2,...,matrix_M) |
short call |
max_var_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 VaR Risk for Loss function is calculated as follows
,
where:
is VaR Risk 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 VaR function.
Remarks
Data for calculation of Maximum VaR Risk 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 , Maximum CVaR for Gain, Maximum CVaR Deviation, Maximum CVaR Deviation for Gain, Maximum VaR for Gain, Maximum VaR Deviation, Maximum VaR Deviation for Gain