%This m-file demonstrates the first optimization setup minimizing outcome
%spread payments for the given CDO portfolio subject to a risk constraint
%assuring the rating of a tranche, single-period default probability
%constraints, and linear constraints on attachment points.

clc
clear;

%Load data from file:
load('Data_for_Step-up_CDO_I_Toolbox.mat');
tbpsg_export_to_workspace(toolboxstruc_arr);

N_attach_points = 5;
%Specify the set of values of upper bound on probability that the
%cumulative collateral loss exceeds the tranche attachment point
%at least once in periods 1,…, T). Columns correspond to credit rating
%(BBB, A, AA, AAA)
Param_Mult_Prob = [0.0281 0.0071 0.0036 0.0012];

%Specify the set of values of upper bound on single-period
%default probability. Rows correspond to credit rating (BBB, A, AA, AAA),
%and columns correspond to the single-periods
Param_Single_Prob = [0.0053018868 0.0106037736 0.0159056604 0.0227981132 0.0281;...
                     0.0013396226 0.0026792453 0.0040188679 0.0057603774 0.0071;...
                     0.0006792453 0.0013584904 0.0020377358 0.0029207547 0.0036;...
                     0.0002264151 0.0004528302 0.0006792453 0.0009735849 0.0012];


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Optimization Problem 1 (Example 1,Case 1)  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Generate fragments of the problem description common for all parameter 
%values within Optimization Problem 1 (Example 1,Case 1)
str1 = sprintf('Problem: problem_example_1_case_1, type = minimize'); 
str2 = sprintf('Objective: objective_linear_sum_of_x_5, linearize = 0');
str3 = sprintf('  linear_sum_of_x_5(matrix_sum_of_x_5)');
str5 = sprintf('  prmulti_pen_5_periods(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)');
str6 = sprintf('Box: >= point_lowerbounds, <= point_upperbounds');
str7 = sprintf('Solver: VAN, precision = 9');

%Begin loop for Optimization Problem 1 (Example 1,Case 1) over parameter values  
for i=1:1:length(Param_Mult_Prob)

%Generate parameter-specific fragment of the problem description
    str4 = sprintf('%s%.7f','Constraint: constraint_mult_prob, upper_bound =  ',Param_Mult_Prob(i));
    
%Generate problem statement
    clear problem_statement;
    problem_statement = sprintf('%s\n', str1, str2, str3, str4, str5, str6, str7);

%Uncomment the following line to open the problem in Toolbox Window:
%tbpsg_toolbox(problem_statement,toolboxstruc_arr);

%Optimize the problem      
    [solution_str, outargstruc_arr] = tbpsg_run(problem_statement, toolboxstruc_arr);
    
%Extract optimal solution   
     point_variables = tbpsg_optimal_point_vars(solution_str, outargstruc_arr);
     loc = tbpsg_optimal_point_data(solution_str, outargstruc_arr);
     Points_Problem_1(:,i) = loc';
     Sum_Attach_Points_Problem_1(i) = tbpsg_objective(solution_str, outargstruc_arr); 
     Multiple_Probabilities_Problem_1(i) = tbpsg_constraints_data(solution_str, outargstruc_arr);
     
     toolboxstruc_arr(size(toolboxstruc_arr,2)+1) = tbpsg_point_pack(['point_opt_point_Problem_1_' int2str(i)],loc,point_variables);
     Constr_period1_Problem_1(i) = tbpsg_function_value('  pr_pen_period1(0.0, matrix_10000_1)', ['point_opt_point_Problem_1_' int2str(i)], toolboxstruc_arr);
     Constr_period2_Problem_1(i) = tbpsg_function_value('  prmulti_pen_period2(0.0,matrix_10000_1,matrix_10000_2)', ['point_opt_point_Problem_1_' int2str(i)], toolboxstruc_arr);
     Constr_period3_Problem_1(i) = tbpsg_function_value('  prmulti_pen_period3(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3)', ['point_opt_point_Problem_1_' int2str(i)], toolboxstruc_arr);
     Constr_period4_Problem_1(i) = tbpsg_function_value('  prmulti_pen_period4(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4)', ['point_opt_point_Problem_1_' int2str(i)], toolboxstruc_arr);
     Constr_period5_Problem_1(i) = tbpsg_function_value('  prmulti_pen_period5(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)', ['point_opt_point_Problem_1_' int2str(i)], toolboxstruc_arr);
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Optimization Problem 2 (Example 1,Case 2)  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Generate fragments of the problem description common for all parameter 
%values within Optimization Problem 2 (Example 1,Case 2)
str1 = sprintf('Problem: problem_example_1_case_2, type = minimize'); 
str2 = sprintf('Objective: objective_linear_sum_of_x_5, linearize = 0');
str3 = sprintf('  linear_sum_of_x_5(matrix_sum_of_x_5)');
str5 = sprintf('  prmulti_pen_5_periods(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)');
str6 = sprintf('Constraint: constraint_x1_x2, lower_bound = 0, upper_bound = 0, linearize = 0');
str7 = sprintf('  linear_x1_x2(matrix_x1_x2)'); 
str8 = sprintf('Constraint: constraint_x2_x3, lower_bound = 0, upper_bound = 0, linearize = 0');
str9 = sprintf('  linear_x2_x3(matrix_x2_x3)'); 
str10 = sprintf('Constraint: constraint_x3_x4, lower_bound = 0, upper_bound = 0, linearize = 0');
str11 = sprintf('  linear_x3_x4(matrix_x3_x4)'); 
str12 = sprintf('Constraint: constraint_x4_x5, lower_bound = 0, upper_bound = 0, linearize = 0');
str13 = sprintf('  linear_x4_x5(matrix_x4_x5)'); 
str14 = sprintf('Box: >= point_lowerbounds, <= point_upperbounds');
str15 = sprintf('Solver: VAN, precision = 9');

%Begin loop for Optimization Problem 2 (Example 1,Case 2) over parameter values  
for i=1:1:length(Param_Mult_Prob)

%Generate parameter-specific fragment of the problem description
    str4 = sprintf('%s%.7f','Constraint: constraint_mult_prob, upper_bound =  ',Param_Mult_Prob(i));
    
%Generate problem statement
    clear problem_statement;
    problem_statement = sprintf('%s\n', str1, str2, str3, str4, str5, str6, str7,...
        str8, str9, str10, str11, str12, str13, str14,str15);

%Uncomment the following line to open the problem in Toolbox Window:
%tbpsg_toolbox(problem_statement,toolboxstruc_arr);

%Optimize the problem      
    [solution_str, outargstruc_arr] = tbpsg_run(problem_statement, toolboxstruc_arr);
    
     point_variables = tbpsg_optimal_point_vars(solution_str, outargstruc_arr);
     loc = tbpsg_optimal_point_data(solution_str, outargstruc_arr);
     Points_Problem_2(:,i) = loc';
     Sum_Attach_Points_Problem_2(i) = tbpsg_objective(solution_str, outargstruc_arr); 
     constr_data = tbpsg_constraints_data(solution_str, outargstruc_arr);
     Multiple_Probabilities_Problem_2(i) = constr_data(1);
      
     toolboxstruc_arr(size(toolboxstruc_arr,2)+1) = tbpsg_point_pack(['point_opt_point_Problem_2_' int2str(i)],loc,point_variables);
     Constr_period1_Problem_2(i) = tbpsg_function_value('pr_pen_period1(0.0, matrix_10000_1)', ['point_opt_point_Problem_2_' int2str(i)], toolboxstruc_arr);
     Constr_period2_Problem_2(i) = tbpsg_function_value('prmulti_pen_period2(0.0,matrix_10000_1,matrix_10000_2)', ['point_opt_point_Problem_2_' int2str(i)], toolboxstruc_arr);
     Constr_period3_Problem_2(i) = tbpsg_function_value('prmulti_pen_period3(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3)', ['point_opt_point_Problem_2_' int2str(i)], toolboxstruc_arr);
     Constr_period4_Problem_2(i) = tbpsg_function_value('prmulti_pen_period4(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4)', ['point_opt_point_Problem_2_' int2str(i)], toolboxstruc_arr);
     Constr_period5_Problem_2(i) = tbpsg_function_value('prmulti_pen_period5(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)', ['point_opt_point_Problem_2_' int2str(i)], toolboxstruc_arr);

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     Optimization Problem 3 (Example 2)     %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Generate fragments of the problem description common for all parameter 
%values within Optimization Problem 3 (Example 2)
str1 = sprintf('Problem: problem_example_2, type = minimize');
str2 = sprintf('Objective: objective_problem_3');
str3 = sprintf('  0.966736489*pm_pen_g_period_1(0.0, matrix_10000_1)');
str4 = sprintf('  +0.903492046*pm_pen_g_period_2(0.0, matrix_10000_2)');
str5 = sprintf('  +0.84438509*pm_pen_g_period_3(0.0, matrix_10000_3)');
str6 = sprintf('  +0.789144944*pm_pen_g_period_4(0.0, matrix_10000_4)');
str7 = sprintf('  +0.737518639*pm_pen_g_period_5(0.0, matrix_10000_5)');
str9 = sprintf('  pr_pen_period1(0.0, matrix_10000_1)');
str11 = sprintf('  prmulti_pen_period2(0.0,matrix_10000_1,matrix_10000_2)');
str13 = sprintf('  prmulti_pen_period3(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3)');
str15 = sprintf('  prmulti_pen_period4(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4)');
str17 = sprintf('  prmulti_pen_period5(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)');
str18 = sprintf('Box: >= point_lowerbounds, <= point_upperbounds');
str19 = sprintf('Solver: VAN, precision = 9');

%Begin loop for Optimization Problem 3 (Example 2) over parameter values  
for i=1:1:size(Param_Single_Prob,1)

%Generate parameter-specific fragments of the problem description
    str8 = sprintf('%s%.10f','Constraint: constraint_period1, upper_bound =  ',Param_Single_Prob(i,1));
    str10 = sprintf('%s%.10f','Constraint: constraint_period2, upper_bound =  ',Param_Single_Prob(i,2));
    str12 = sprintf('%s%.10f','Constraint: constraint_period3, upper_bound =  ',Param_Single_Prob(i,3));
    str14 = sprintf('%s%.10f','Constraint: constraint_period4, upper_bound =  ',Param_Single_Prob(i,4));
    str16 = sprintf('%s%.10f','Constraint: constraint_period5, upper_bound =  ',Param_Single_Prob(i,5));

%Generate problem statement
    clear problem_statement;
    problem_statement = sprintf('%s\n', str1, str2, str3, str4, str5, str6, str7,...
    str8, str9, str10, str11, str12, str13, str14, str15, str16, str17, str18, str19);

%Uncomment the following line to open the problem in Toolbox Window:
%tbpsg_toolbox(problem_statement,toolboxstruc_arr);

%Optimize the problem      
    [solution_str, outargstruc_arr] = tbpsg_run(problem_statement, toolboxstruc_arr);
    
%Extract optimal solution   
     point_variables = tbpsg_optimal_point_vars(solution_str, outargstruc_arr);
     loc = tbpsg_optimal_point_data(solution_str, outargstruc_arr);
     Points_Problem_3(:,i)= loc';
     Obj_Problem_3(i) = tbpsg_objective(solution_str, outargstruc_arr); 
          
     toolboxstruc_arr(size(toolboxstruc_arr,2)+1) = tbpsg_point_pack(['point_opt_point_Problem_3_' int2str(i)],loc,point_variables);
     Constr_period1_Problem_3(i) = tbpsg_function_value('pr_pen_period1(0.0, matrix_10000_1)', ['point_opt_point_Problem_3_' int2str(i)], toolboxstruc_arr);
     Constr_period2_Problem_3(i) = tbpsg_function_value('prmulti_pen_period2(0.0,matrix_10000_1,matrix_10000_2)', ['point_opt_point_Problem_3_' int2str(i)], toolboxstruc_arr);
     Constr_period3_Problem_3(i) = tbpsg_function_value('prmulti_pen_period3(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3)', ['point_opt_point_Problem_3_' int2str(i)], toolboxstruc_arr);
     Constr_period4_Problem_3(i) = tbpsg_function_value('prmulti_pen_period4(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4)', ['point_opt_point_Problem_3_' int2str(i)], toolboxstruc_arr);
     Constr_period5_Problem_3(i) = tbpsg_function_value('prmulti_pen_period5(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)', ['point_opt_point_Problem_3_' int2str(i)], toolboxstruc_arr);
     
     Multiple_Probabilities_Problem_3(i) = Constr_period5_Problem_3(i);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Optimization Problem 4 (Example 3, case 1) %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Generate fragments of the problem description common for all parameter 
%values within Optimization Problem 4 (Example 3, case 1)
str1 = sprintf('Problem: problem_example_3_case_1, type = minimize');
str2 = sprintf('Objective: objective_problem_4');
str3 = sprintf('0.966736489*pm_pen_g_period_1(0.0, matrix_10000_1)');
str4 = sprintf('+0.903492046*pm_pen_g_period_2(0.0, matrix_10000_2)');
str5 = sprintf('+0.84438509*pm_pen_g_period_3(0.0, matrix_10000_3)');
str6 = sprintf('+0.789144944*pm_pen_g_period_4(0.0, matrix_10000_4)');
str7 = sprintf('+0.737518639*pm_pen_g_period_5(0.0, matrix_10000_5)');
str9 = sprintf('prmulti_pen_5_periods(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)');
str10 = sprintf('Box: >= point_lowerbounds, <= point_upperbounds');
str11 = sprintf('Solver: VAN, precision = 9');

%Begin loop for Optimization Problem 4 (Example 3,Case 1) over parameter values  
for i=1:1:length(Param_Mult_Prob)

%Generate parameter-specific fragment of the problem description
    str8 = sprintf('%s%.7f','Constraint: constraint_mult_prob, upper_bound =  ',Param_Mult_Prob(i));
    
%Generate problem statement
    clear problem_statement;
    problem_statement = sprintf('%s\n', str1, str2, str3, str4, str5, str6, str7,...
                              str8, str9, str10, str11);

%Uncomment the following line to open the problem in Toolbox Window:
%tbpsg_toolbox(problem_statement,toolboxstruc_arr);                          
                          
%Optimize the problem      
    [solution_str, outargstruc_arr] = tbpsg_run(problem_statement, toolboxstruc_arr);
    
%Extract optimal solution   
     point_variables = tbpsg_optimal_point_vars(solution_str, outargstruc_arr);
     loc = tbpsg_optimal_point_data(solution_str, outargstruc_arr);
     Points_Problem_4(:,i)= loc';
     Obj_Problem_4(i) = tbpsg_objective(solution_str, outargstruc_arr); 
     constr_data = tbpsg_constraints_data(solution_str, outargstruc_arr);
     Multiple_Probabilities_Problem_4(i) = constr_data(1);
     
     toolboxstruc_arr(size(toolboxstruc_arr,2)+1) = tbpsg_point_pack(['point_opt_point_Problem_4_' int2str(i)],loc,point_variables);
     Constr_period1_Problem_4(i) = tbpsg_function_value('pr_pen_period1(0.0, matrix_10000_1)', ['point_opt_point_Problem_4_' int2str(i)], toolboxstruc_arr);
     Constr_period2_Problem_4(i) = tbpsg_function_value('prmulti_pen_period2(0.0,matrix_10000_1,matrix_10000_2)', ['point_opt_point_Problem_4_' int2str(i)], toolboxstruc_arr);
     Constr_period3_Problem_4(i) = tbpsg_function_value('prmulti_pen_period3(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3)', ['point_opt_point_Problem_4_' int2str(i)], toolboxstruc_arr);
     Constr_period4_Problem_4(i) = tbpsg_function_value('prmulti_pen_period4(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4)', ['point_opt_point_Problem_4_' int2str(i)], toolboxstruc_arr);
     Constr_period5_Problem_4(i) = tbpsg_function_value('prmulti_pen_period5(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)', ['point_opt_point_Problem_4_' int2str(i)], toolboxstruc_arr);

end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Optimization Problem 5 (Example 3, case 2) %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Generate fragments of the problem description common for all parameter 
%values within Optimization Problem 5 (Example 3, case 2)
str1 = sprintf('Problem: problem_example_3_case_2, type = minimize');
str2 = sprintf('Objective: objective_problem_5');
str3 = sprintf('0.966736489*pm_pen_g_period_1(0.0, matrix_10000_1)');
str4 = sprintf('+0.903492046*pm_pen_g_period_2(0.0, matrix_10000_2)');
str5 = sprintf('+0.84438509*pm_pen_g_period_3(0.0, matrix_10000_3)');
str6 = sprintf('+0.789144944*pm_pen_g_period_4(0.0, matrix_10000_4)');
str7 = sprintf('+0.737518639*pm_pen_g_period_5(0.0, matrix_10000_5)');
str9 = sprintf('prmulti_pen_5_periods(0.00000000,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)');
str10 = sprintf('Constraint: constraint_x1_x2, lower_bound = 0, upper_bound = 0, linearize = 0');
str11 = sprintf('linear_x1_x2(matrix_x1_x2)');
str12 = sprintf('Constraint: constraint_x2_x3, lower_bound = 0, upper_bound = 0, linearize = 0');
str13 = sprintf('linear_x2_x3(matrix_x2_x3)');
str14 = sprintf('Constraint: constraint_x3_x4, lower_bound = 0, upper_bound = 0, linearize = 0');
str15 = sprintf('linear_x3_x4(matrix_x3_x4)');
str16 = sprintf('Constraint: constraint_x4_x5, lower_bound = 0, upper_bound = 0, linearize = 0');
str17 = sprintf('linear_x4_x5(matrix_x4_x5)');
str18 = sprintf('Box: >= point_lowerbounds, <= point_upperbounds');
str19 = sprintf('Solver: VAN, precision = 9');

%Begin loop for Optimization Problem 5 (Example 3,Case 2) over parameter values  
for i=1:1:length(Param_Mult_Prob)

%Generate parameter-specific fragment of the problem description
    str8 = sprintf('%s%.7f','Constraint: constraint_mult_prob, upper_bound =  ',Param_Mult_Prob(i));
    
%Generate problem statement
    clear problem_statement;
    problem_statement = sprintf('%s\n', str1, str2, str3, str4, str5, str6, str7,...
     str8, str9, str10, str11, str12, str13, str14, str15, str16, str17, str18, str19);

%Uncomment the following line to open the problem in Toolbox Window:
%tbpsg_toolbox(problem_statement,toolboxstruc_arr);
 
 %Optimize the problem      
    [solution_str, outargstruc_arr] = tbpsg_run(problem_statement, toolboxstruc_arr);
    
%Extract optimal solution   
     point_variables = tbpsg_optimal_point_vars(solution_str, outargstruc_arr);
     loc = tbpsg_optimal_point_data(solution_str, outargstruc_arr);
     Points_Problem_5(:,i)= loc';
     Obj_Problem_5(i) = tbpsg_objective(solution_str, outargstruc_arr);
     constr_data = tbpsg_constraints_data(solution_str, outargstruc_arr);
     Multiple_Probabilities_Problem_5(i) = constr_data(1);
     
     toolboxstruc_arr(size(toolboxstruc_arr,2)+1) = tbpsg_point_pack(['point_opt_point_Problem_5_' int2str(i)],loc,point_variables);
     Constr_period1_Problem_5(i) = tbpsg_function_value('pr_pen_period1(0.0, matrix_10000_1)', ['point_opt_point_Problem_5_' int2str(i)], toolboxstruc_arr);
     Constr_period2_Problem_5(i) = tbpsg_function_value('prmulti_pen_period2(0.0,matrix_10000_1,matrix_10000_2)', ['point_opt_point_Problem_5_' int2str(i)], toolboxstruc_arr);
     Constr_period3_Problem_5(i) = tbpsg_function_value('prmulti_pen_period3(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3)', ['point_opt_point_Problem_5_' int2str(i)], toolboxstruc_arr);
     Constr_period4_Problem_5(i) = tbpsg_function_value('prmulti_pen_period4(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4)', ['point_opt_point_Problem_5_' int2str(i)], toolboxstruc_arr);
     Constr_period5_Problem_5(i) = tbpsg_function_value('prmulti_pen_period5(0.0,matrix_10000_1,matrix_10000_2,matrix_10000_3,matrix_10000_4,matrix_10000_5)', ['point_opt_point_Problem_5_' int2str(i)], toolboxstruc_arr);

end

warning('on', 'all');

str_ = ['BBB ' 'A ' 'AA ' 'AAA '];
ratings = strread(str_, '%s');
clear str_;

str_ = ['Attachment_Point_1 ' 'Attachment_Point_2 ' 'Attachment_Point_3 ' 'Attachment_Point_4 ' 'Attachment_Point_5 ' ];
attach_points_names = strread(str_, '%s');
attach_points_names = strrep(attach_points_names, '_', ' ');
clear str_;

str_ = ['Attach._Point_1 ' 'Attach._Point_2 ' 'Attach._Point_3 ' 'Attach._Point_4 ' 'Attach._Point_5 ' ];
attach_points_names_graph = strread(str_, '%s');
attach_points_names_graph = strrep(attach_points_names_graph, '_', ' ');
clear str_;

str_ = ['Problem_1 ' 'Problem_2 ' 'Problem_3 ' 'Problem_4 ' 'Problem_5 ' ];
problems_names = strread(str_, '%s');
problems_names = strrep(problems_names, '_', ' ');
clear str_;

str_ = ['Linear_Objective_(Problem_1) ' 'Linear_Objective_(Problem_2) ' ...
    'Partial_Moment_Objective_(Problem_3) ' 'Partial_Moment_Objective_(Problem_4) '...
    'Partial_Moment_Objective_(Problem_5) '];
objectives_names = strread(str_, '%s');
objectives_names = strrep(objectives_names, '_', ' ');
clear str_;

str_ = ['period_t=1 ' 'period_t=2 ' 'period_t=3 ' 'period_t=4 ' 'period_t=5 '];
period_names = strread(str_, '%s');
period_names = strrep(period_names, '_', ' ');
clear str_;

% display and save tables with results of calculations
outfilename = 'Step-up_CDO_I_Output_Short.txt';
fid = fopen(outfilename, 'w');


fprintf('Table 1. Example 1, Case 1: Attachment Points vs. Rating\n');
fprintf(fid, 'Table 1. Example 1, Case 1: Attachment Points vs. Rating\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid, 'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:N_attach_points
        fprintf('%16f',Points_Problem_1(j,i));
        fprintf(fid,'%16f',Points_Problem_1(j,i));
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 2. Example 1, Case 2: Attachment Points vs. Rating\n');
fprintf(fid,'Table 2. Example 1, Case 2: Attachment Points vs. Rating\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid,'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:N_attach_points
        fprintf('%16f',Points_Problem_2(j,i));
        fprintf(fid,'%16f',Points_Problem_2(j,i));
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 3. Example 2: Attachment Points vs. Rating\n');
fprintf(fid,'Table 3. Example 2: Attachment Points vs. Rating\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid,'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:N_attach_points
        fprintf('%16f',Points_Problem_3(j,i));
        fprintf(fid,'%16f',Points_Problem_3(j,i));
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 4. Example 3, Case 1: Attachment Points vs. Rating\n');
fprintf(fid,'Table 4. Example 3, Case 1: Attachment Points vs. Rating\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid,'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:N_attach_points
        fprintf('%16f',Points_Problem_4(j,i));
        fprintf(fid,'%16f',Points_Problem_4(j,i));
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 5. Example 3, Case 2: Attachment Points vs. Rating\n');
fprintf(fid,'Table 5. Example 3, Case 2: Attachment Points vs. Rating\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid,'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:N_attach_points
        fprintf('%16f',Points_Problem_5(j,i));
        fprintf(fid,'%16f',Points_Problem_5(j,i));
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 6. Comparison of Attachment Points:  Example 1, Case 1 vs. Example 3, Case 1\n');
fprintf(fid,'Table 6. Comparison of Attachment Points:  Example 1, Case 1 vs. Example 3, Case 1\n');
fprintf('Rating   Attachment Points   Example 1,Case 1   Example 3,Case 1   Discrepancy\n');
fprintf(fid,'Rating   Attachment Points   Example 1,Case 1   Example 3,Case 1   Discrepancy\n');
for i=1:1:length(Param_Mult_Prob)
    for j=1:1:N_attach_points
        fprintf('%5s%21s%16f%17f%17f%s',ratings{i}, attach_points_names{j},...
            Points_Problem_1(j,i), Points_Problem_4(j,i),...
            100*abs(Points_Problem_4(j,i)-Points_Problem_1(j,i))/Points_Problem_1(j,i),'%');
        fprintf(fid,'%5s%21s%16f%17f%17f%s',ratings{i}, attach_points_names{j},...
            Points_Problem_1(j,i), Points_Problem_4(j,i),...
            100*abs(Points_Problem_4(j,i)-Points_Problem_1(j,i))/Points_Problem_1(j,i),'%');
        fprintf('\n');
        fprintf(fid,'\n');
    end
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 7. Comparison of Attachment Points:  Example 1, Case 2 vs. Example 3, Case 2\n');
fprintf(fid,'Table 7. Comparison of Attachment Points:  Example 1, Case 2 vs. Example 3, Case 2\n');
fprintf('Rating   Attachment Points   Example 1,Case 2   Example 3,Case 2   Discrepancy\n');
fprintf(fid,'Rating   Attachment Points   Example 1,Case 2   Example 3,Case 2   Discrepancy\n');
for i=1:1:length(Param_Mult_Prob)
    for j=1:1:N_attach_points
        fprintf('%5s%21s%16f%17f%17f%s',ratings{i}, attach_points_names{j},...
            Points_Problem_2(j,i), Points_Problem_5(j,i),...
            100*abs(Points_Problem_5(j,i)-Points_Problem_2(j,i))/Points_Problem_2(j,i),'%');
        fprintf(fid,'%5s%21s%16f%17f%17f%s',ratings{i}, attach_points_names{j},...
            Points_Problem_2(j,i), Points_Problem_5(j,i),...
            100*abs(Points_Problem_5(j,i)-Points_Problem_2(j,i))/Points_Problem_2(j,i),'%');
        fprintf('\n');
        fprintf(fid,'\n');
    end
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 8. Default Probabilities of CDO Tranche vs. Ratings for Problems 1 - 5\n');
fprintf(fid,'Table 8. Default Probabilities of CDO Tranche vs. Ratings for Problems 1 - 5\n');
fprintf('Rating  Problem 1  Problem 2  Problem 3  Problem 4  Problem 5\n');
fprintf(fid,'Rating  Problem 1  Problem 2  Problem 3  Problem 4  Problem 5\n');
for i=1:1:length(Param_Mult_Prob)
   fprintf('%5s%11f%11f%11f%11f%11f\n',ratings{i},Multiple_Probabilities_Problem_1(i),...
            Multiple_Probabilities_Problem_2(i), Multiple_Probabilities_Problem_3(i),...
            Multiple_Probabilities_Problem_4(i), Multiple_Probabilities_Problem_5(i));
   fprintf(fid,'%5s%11f%11f%11f%11f%11f\n',ratings{i},Multiple_Probabilities_Problem_1(i),...
            Multiple_Probabilities_Problem_2(i), Multiple_Probabilities_Problem_3(i),...
            Multiple_Probabilities_Problem_4(i), Multiple_Probabilities_Problem_5(i));
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 9. Single-Period Default Probabilities in Problem 1\n');
fprintf(fid,'Table 9. Single-Period Default Probabilities in Problem 1\n');
fprintf('Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
fprintf(fid,'Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
for i=1:1:length(Param_Mult_Prob)
   fprintf('%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_1(i),...
            Constr_period2_Problem_1(i)-Constr_period1_Problem_1(i),...
            Constr_period3_Problem_1(i)-Constr_period2_Problem_1(i),...
            Constr_period4_Problem_1(i)-Constr_period3_Problem_1(i),...
            Constr_period5_Problem_1(i)-Constr_period4_Problem_1(i));
   fprintf(fid,'%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_1(i),...
            Constr_period2_Problem_1(i)-Constr_period1_Problem_1(i),...
            Constr_period3_Problem_1(i)-Constr_period2_Problem_1(i),...
            Constr_period4_Problem_1(i)-Constr_period3_Problem_1(i),...
            Constr_period5_Problem_1(i)-Constr_period4_Problem_1(i));

end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 10. Single-Period Default Probabilities in Problem 2\n');
fprintf(fid,'Table 10. Single-Period Default Probabilities in Problem 2\n');
fprintf('Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
fprintf(fid,'Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
for i=1:1:length(Param_Mult_Prob)
   fprintf('%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_2(i),...
            Constr_period2_Problem_2(i)-Constr_period1_Problem_2(i),...
            Constr_period3_Problem_2(i)-Constr_period2_Problem_2(i),...
            Constr_period4_Problem_2(i)-Constr_period3_Problem_2(i),...
            Constr_period5_Problem_2(i)-Constr_period4_Problem_2(i));
   fprintf(fid,'%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_2(i),...
            Constr_period2_Problem_2(i)-Constr_period1_Problem_2(i),...
            Constr_period3_Problem_2(i)-Constr_period2_Problem_2(i),...
            Constr_period4_Problem_2(i)-Constr_period3_Problem_2(i),...
            Constr_period5_Problem_2(i)-Constr_period4_Problem_2(i));
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 11. Single-Period Default Probabilities in Problem 3\n');
fprintf(fid,'Table 11. Single-Period Default Probabilities in Problem 3\n');
fprintf('Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
fprintf(fid,'Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
for i=1:1:length(Param_Mult_Prob)
   fprintf('%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_3(i),...
            Constr_period2_Problem_3(i)-Constr_period1_Problem_3(i),...
            Constr_period3_Problem_3(i)-Constr_period2_Problem_3(i),...
            Constr_period4_Problem_3(i)-Constr_period3_Problem_3(i),...
            Constr_period5_Problem_3(i)-Constr_period4_Problem_3(i));
   fprintf(fid,'%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_3(i),...
            Constr_period2_Problem_3(i)-Constr_period1_Problem_3(i),...
            Constr_period3_Problem_3(i)-Constr_period2_Problem_3(i),...
            Constr_period4_Problem_3(i)-Constr_period3_Problem_3(i),...
            Constr_period5_Problem_3(i)-Constr_period4_Problem_3(i));
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 12. Single-Period Default Probabilities in Problem 4\n');
fprintf(fid,'Table 12. Single-Period Default Probabilities in Problem 4\n');
fprintf('Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
fprintf(fid,'Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
for i=1:1:length(Param_Mult_Prob)
   fprintf('%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_3(i),...
            Constr_period2_Problem_4(i)-Constr_period1_Problem_4(i),...
            Constr_period3_Problem_4(i)-Constr_period2_Problem_4(i),...
            Constr_period4_Problem_4(i)-Constr_period3_Problem_4(i),...
            Constr_period5_Problem_4(i)-Constr_period4_Problem_4(i));
   fprintf(fid,'%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_3(i),...
            Constr_period2_Problem_4(i)-Constr_period1_Problem_4(i),...
            Constr_period3_Problem_4(i)-Constr_period2_Problem_4(i),...
            Constr_period4_Problem_4(i)-Constr_period3_Problem_4(i),...
            Constr_period5_Problem_4(i)-Constr_period4_Problem_4(i));
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 13. Single-Period Default Probabilities in Problem 5\n');
fprintf(fid,'Table 13. Single-Period Default Probabilities in Problem 5\n');
fprintf('Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
fprintf(fid,'Rating  Period 1  Period 2  Period 3  Period 4  Period 5\n');
for i=1:1:length(Param_Mult_Prob)
   fprintf('%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_3(i),...
            Constr_period2_Problem_5(i)-Constr_period1_Problem_5(i),...
            Constr_period3_Problem_5(i)-Constr_period2_Problem_5(i),...
            Constr_period4_Problem_5(i)-Constr_period3_Problem_5(i),...
            Constr_period5_Problem_5(i)-Constr_period4_Problem_5(i));
   fprintf(fid,'%5s%11f%10f%10f%10f%10f\n',ratings{i},Constr_period1_Problem_3(i),...
            Constr_period2_Problem_5(i)-Constr_period1_Problem_5(i),...
            Constr_period3_Problem_5(i)-Constr_period2_Problem_5(i),...
            Constr_period4_Problem_5(i)-Constr_period3_Problem_5(i),...
            Constr_period5_Problem_5(i)-Constr_period4_Problem_5(i));
end
fprintf('\n');
fprintf(fid,'\n');

% display Attachment Points for Example 1, Case 1
figure
bar(Points_Problem_1,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'NorthWest');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for the Optimal Solution of Problem 1 ');


% display Attachment Points for Example 1, Case 2
figure
bar(Points_Problem_2,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'EastOutside');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for the Optimal Solution of Problem 2 ');


% display Attachment Points for Example 2
figure
bar(Points_Problem_3,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'NorthWest');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for the Optimal Solution of Problem 3 ');


% display Attachment Points for Example 3, Case 1
figure
bar(Points_Problem_4,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'NorthWest');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for the Optimal Solution of Problem 4 ');


% display Attachment Points for Example 3, Case 2
figure
bar(Points_Problem_5,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'EastOutside');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for the Optimal Solution of Problem 5 ');


% display Default Probabilities of CDO Tranche vs. Ratings 
Y = [Multiple_Probabilities_Problem_1' Multiple_Probabilities_Problem_2'...
    Multiple_Probabilities_Problem_3' Multiple_Probabilities_Problem_4' Multiple_Probabilities_Problem_5'];
figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(ratings));
hAxes = gca;
set(hAxes, 'XTickLabel', ratings);
grid on;
legend(problems_names, 'Location', 'EastOutside');
xlabel('Ratings');
ylabel('Default Probabilities of CDO Tranche');
title('Default Probabilities of CDO Tranche vs. Ratings ');
clear Y;


% display optimal linear objective values obtained in Problem 1, Problem 2,
% and optimal partial moment functions objective values obtained in 
% Problem 3, Problem 4, and Problem 5

Y = [Sum_Attach_Points_Problem_1' Sum_Attach_Points_Problem_2'...
    Obj_Problem_3' Obj_Problem_4' Obj_Problem_5'];
figure
plot(Y);
  set(gca,'XTick',1:1:length(ratings));
hAxes = gca;
set(hAxes, 'XTickLabel', ratings);
grid on;
legend(objectives_names, 'Location', 'EastOutside');
%xlabel('Names of Attachment Points');
ylabel('Credit Ratings');
title('Optimal Objective Values ');
title('Default Probabilities of CDO Tranche vs. Ratings ');
clear Y;


% display dependence of single-period default probabilities for a tranche at
% period t = 1,…, 5,  vs. ratings for Problem 1 
Y = [Constr_period1_Problem_1' Constr_period2_Problem_1'-Constr_period1_Problem_1'...
    Constr_period3_Problem_1'-Constr_period2_Problem_1'...
    Constr_period4_Problem_1'-Constr_period3_Problem_1'...
    Constr_period5_Problem_1'-Constr_period4_Problem_1'];
figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(ratings));
hAxes = gca;
set(hAxes, 'XTickLabel', ratings);
grid on;
legend(period_names, 'Location', 'EastOutside');
xlabel('Ratings');
ylabel('Single-Period Default Probabilities');
title('Single-Period Default Probabilities vs. Ratings for Problem 1 ');
clear Y;

% display dependence of single-period default probabilities for a tranche at
% period t = 1,…, 5,  vs. ratings for Problem 2 
Y = [Constr_period1_Problem_2' Constr_period2_Problem_2'-Constr_period1_Problem_2'...
    Constr_period3_Problem_2'-Constr_period2_Problem_2'...
    Constr_period4_Problem_2'-Constr_period3_Problem_2'...
    Constr_period5_Problem_2'-Constr_period4_Problem_2'];
figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(ratings));
hAxes = gca;
set(hAxes, 'XTickLabel', ratings);
grid on;
legend(period_names, 'Location', 'EastOutside');
xlabel('Ratings');
ylabel('Single-Period Default Probabilities');
title('Single-Period Default Probabilities vs. ratings for Problem 2 ');
clear Y;


% display dependence of single-period default probabilities for a tranche at
% period t = 1,…, 5,  vs. ratings for Problem 3 
Y = [Constr_period1_Problem_3' Constr_period2_Problem_3'-Constr_period1_Problem_3'...
    Constr_period3_Problem_3'-Constr_period2_Problem_3'...
    Constr_period4_Problem_3'-Constr_period3_Problem_3'...
    Constr_period5_Problem_3'-Constr_period4_Problem_3'];
figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(ratings));
hAxes = gca;
set(hAxes, 'XTickLabel', ratings);
grid on;
legend(period_names, 'Location', 'EastOutside');
xlabel('Ratings');
ylabel('Single-Period Default Probabilities');
title('Single-Period Default Probabilities vs. ratings for Problem 3 ');
clear Y;


% display dependence of single-period default probabilities for a tranche at
% period t = 1,…, 5,  vs. ratings for Problem 4 
Y = [Constr_period1_Problem_4' Constr_period2_Problem_4'-Constr_period1_Problem_4'...
    Constr_period3_Problem_4'-Constr_period2_Problem_4'...
    Constr_period4_Problem_4'-Constr_period3_Problem_4'...
    Constr_period5_Problem_4'-Constr_period4_Problem_4'];
figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(ratings));
hAxes = gca;
set(hAxes, 'XTickLabel', ratings);
grid on;
legend(period_names, 'Location', 'EastOutside');
xlabel('Ratings');
ylabel('Single-Period Default Probabilities');
title('Single-Period Default Probabilities vs. ratings for Problem 4 ');
clear Y;


% display dependence of single-period default probabilities for a tranche at
% period t = 1,…, 5,  vs. ratings for Problem 5 
Y = [Constr_period1_Problem_5' Constr_period2_Problem_5'-Constr_period1_Problem_5'...
    Constr_period3_Problem_5'-Constr_period2_Problem_5'...
    Constr_period4_Problem_5'-Constr_period3_Problem_5'...
    Constr_period5_Problem_5'-Constr_period4_Problem_5'];
figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(ratings));
hAxes = gca;
set(hAxes, 'XTickLabel', ratings);
grid on;
legend(period_names, 'Location', 'EastOutside');
xlabel('Ratings');
ylabel('Single-Period Default Probabilities');
title('Single-Period Default Probabilities vs. ratings for Problem 5 ');
clear Y;

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