Solution in MATLAB Environment
Contents
Table 1. Solution report for Problem 1
Table 2. Solution report for Problem 2
Case study VaR vs Probability Constraints (see Formal Problem Statement) in MATLAB Environment is solved with riskconstrprog PSG subroutine and include two equivalent problems:
| • | Problem 1 (CS.1 - CS.4): Maximizing estimated return with probability constraint. |
| • | Problem 2 (CS.5 - CS.8): Maximizing estimated return with VaR constraint. |
Let us describe the main operations. To run case study you need to do the following main steps in file problem_MaxRet_Prob.m.
Data are saved in files problem_MaxRet_Prob_data.mat.
Load data:
load('.\problem_MaxRet_Prob_data.mat')
Define options for PSG solver:
stroptions.Precision = 9;
stroptions.Stages = 10;
Define input arguments:
string1 = {};
string2 = {'pr_pen'};
w2 = {0.02};
Optimize problem:
[xout, fval, status, output] = riskconstrprog([], string2, [], [], [], [], w2, H2, [], [], d, r, [], [], Aeq, beq, lb, ub, [], stroptions); |
Display solution:
disp(' ');
disp('Results: ');
Display status of optimization problem:
disp(sprintf('status of optimization problem = %s', status));
Display solving time:
disp(sprintf('solving time = %g', output.solving_time));
Display objective:
disp(sprintf('objective = %g', fval));
Display function:
disp(sprintf('pr_pen= %g', output.frval2))
Display linear component of objective:
disp('linear component of objective:');
disp(output.fdval);
Display left hand sides of linear equality:
disp(sprintf('linear equality = %g', output.fAeqval));
Display residual of linear equality:
disp(sprintf('residual of linear equality = %g', output.rAeqval));
Display optimal point:
disp('optimal point = ');
disp(xout');
Further we describe the main operations in file problem_MaxRet_VaR.m.
Data are saved in files problem_MaxRet_VaR_data.mat.
Load data:
load('.\problem_MaxRet_VaR_data.mat')
Define options for PSG solver:
stroptions.Precision = 9;
stroptions.Stages = 10;
Define input arguments:
string2 = {'var_risk'};
w2 = {0.95};
Optimize problem:
[xout, fval, status, output] = riskconstrprog([], string2, [], [], [], [], w2, H2, [], [], d, r, [], [], Aeq, beq, lb, ub, [], stroptions); |
Display solution:
disp(' ');
disp('Results: ');
Display status of optimization problem:
disp(sprintf('status of optimization problem = %s', status));
Display solving time:
disp(sprintf('solving time = %g', output.solving_time));
Display objective:
disp(sprintf('objective = %g', fval));
Display function:
disp(sprintf('var_risk= %g', output.frval2))
Display linear component of objective:
disp('linear component of objective:');
disp(output.fdval);
Display left hand sides of linear equality:
disp(sprintf('linear equality = %g', output.fAeqval));
Display residual of linear equality:
disp(sprintf('residual of linear equality = %g', output.rAeqval));
Display optimal point:
disp('optimal point = ');
disp(xout');
Table 1. Solution report for Problem 1
Results:
status of optimization problem = optimal
solving time = 0.01
objective = -0.00120185
pr_pen= 0.0264543
linear component of objective:
-0.0012
linear equality = 1
residual of linear equality = 0
optimal point =
0.0506 0.0708 0.0534 0.0792 0.2887 0.0197 0.3002 0.0632 0.0195 0.0547
Table 2. Solution report for Problem 2
Results:
status of optimization problem = optimal
solving time = 0.01
objective = -0.00120185
var_risk= 0.0144691
linear component of objective:
-0.0012
linear equality = 1
residual of linear equality = 0
optimal point =
0.0506 0.0708 0.0534 0.0792 0.2887 0.0197 0.3002 0.0632 0.0195 0.0547