% This case study solves two optimization problems:
% (1) maximizing  annualized portfolio return on multiple sample
% paths subject to constraint on CDaR Deviation Multiple;
% (2) maximizing  annualized portfolio return on a single sample
% path, which is the union of all scenarios extracted from 
% multiple sample paths, subject to constraint on CDaR Deviation.
% Finally, it compares solutions of these two optimization problems. 

clc
clear

%Load data prepared in PSG Toolbox format and packed in structure 'toolboxstruc_arr':
load CS_CDaR_Single_Path_vs_CDaR_Multiple_Paths_Toolbox_data.mat 'toolboxstruc_arr'
tbpsg_export_to_workspace(toolboxstruc_arr);

%Generate problem statement for CDaR Deviation Multiple:
 str1_1 = sprintf('maximize');
 str1_2 = sprintf('linear_average_returns(matrix_average_annualized_returns)');
 str1_3 = sprintf('Constraint: <= 0.023');
 str1_4 = sprintf('cdarmulti_dev(0.8, matrix_1,...,matrix_11)');
 str1_5 = sprintf('Box: >= point_lowerbounds, <= point_upperbounds');
 str1_6 = sprintf('Solver: TANK, precision = 9');
  
clear problem_statement1;
problem_statement1 = sprintf('%s\n', str1_1, str1_2, str1_3, str1_4, str1_5, str1_6);
    
%Optimize the first problem:
[solution_str1, outargstruc_arr1] = tbpsg_run(problem_statement1, toolboxstruc_arr);
%Extract optimal solution:       
point_variables1 = tbpsg_optimal_point_vars(solution_str1, outargstruc_arr1);
Points1 = tbpsg_optimal_point_data(solution_str1, outargstruc_arr1)';


%Generate problem statement for CDaR Deviation Single:

 str2_1 = sprintf('maximize');
 str2_2 = sprintf('linear(matrix_average_annualized_returns)');
 str2_3 = sprintf('Constraint: <= 0.023');
 str2_4 = sprintf('cdar_dev(0.8, matrix_H)');
 str2_5 = sprintf('Box: >= point_lowerbounds, <= point_upperbounds');
 str2_6 = sprintf('Solver: TANK, precision = 9');
  
clear problem_statement2;
problem_statement2 = sprintf('%s\n', str2_1, str2_2, str2_3, str2_4, str2_5, str2_6);
    
%Optimize the second problem:   
[solution_str2, outargstruc_arr2] = tbpsg_run(problem_statement2, toolboxstruc_arr);

%Extract optimal solution:       
point_variables2 = tbpsg_optimal_point_vars(solution_str2, outargstruc_arr2);
Points2 = tbpsg_optimal_point_data(solution_str2, outargstruc_arr2)';
      
%Display table comparing two solutions:
    
fprintf('\n%s','Components   Solution with CDaR_DEV Multiple   Solution with CDaR_DEV Single');
for j=1:size(point_variables2,2)
    fprintf('\n%s\t\t\t\t\t%.4f\t\t\t\t\t\t\t%.4f', point_variables2{j}, Points1(j), Points2(j));
end
fprintf('\n');
    
%Generate graph comparing two solutions.

%Select instruments that have different positions in two optimal solutions:
    i = 0;
    for j=1:size(point_variables2,2)
        if abs(Points1(j)- Points2(j))>1E-6
            i = i + 1;
            point_variables(i) = point_variables2(j);
            Point1(i) = Points1(j);
            Point2(i) = Points2(j);
        end
    end
    Points =[Point1' Point2'];
    str_points = ['CDaR_Dev_Multiple ' 'CDaR_Dev_Single '];
    leg = strread(str_points, '%s'); 
    leg = strrep(leg, '_', ' ');
    figure
    plot(Points,'.', 'MarkerSize',20)
    set(gca,'XTick',1:1:size(point_variables',1));
    hAxes = gca;
    set(hAxes, 'XTickLabel', point_variables');
    grid on;
    legend(leg, 'Location', 'NorthWest');
    xlabel('Instruments Having Different Positions in Two Optimal Solutions');
    ylabel('Value of Position ');
    title('Comparison of Solutions Obtained with CDaR Dev Multiple and CDaR Dev Single');

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