# Case Study: Structuring step up CDO

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Case study background and problem formulations

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.

PROBLEM1: problem_example_1_case_1__BBB
Minimize Linear (minimize upper bound of spread payments over all periods for tranche m)
subject to
Prmulti_pen ≤ Const1 (risk constraint assuring rating of a tranche)
Box constraints (box constraints on attachment points)
——————————————————————–
Prmulti_pen = Probability Exceeding Penalty for Loss Multiple
Box constraints = constraints on individual decision variables
——————————————————————–
Dataset1 5 10,000 0.917241635202 0.27 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 5 500,000 0.924930682919 106.88
PROBLEM2: problem_example_1_case_2__BBB
Minimize Linear (minimize upper bound of spread payments over all periods for tranche m)
subject to
Linearmulti = Const2 (linear constraints)
Prmulti_pen ≤ Const3 (risk constraint assuring rating of a tranche)
Box constraints (box constraints on attachment points)
——————————————————————–
Linearmulti = Linear Multiple
Prmulti_pen = Probability Exceeding Penalty for Loss Multiple
Box constraints = constraints on individual decision variables
——————————————————————–

Dataset1 5 10,000 1.119680810637 1.08 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 5 500,000 1.113539965258 7.63
PROBLEM3: problem_example_2__BBB
Minimize PV (minimize PV of expected spread payments over all periods for tranche m)
subject to
Pr_pen ≤ Const4
Prmulti_pen ≤ Linear (default probabilities constraints at time period t)
Box constraints (box constraints on attachment points)
——————————————————————–
PV = Present Value
Pr_pen = Probability Exceeding Penalty for Loss
Prmulti_pen = Probability Exceeding Penalty for Loss Multiple
Box constraints = constraints on individual decision variables
——————————————————————–

Dataset1 5 10,000 0.588263342701 0.71 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 5 500,000 0.591988749103 137.36

NOTE: Problem statements can be simplified using InnerProduct and a set of matriсes.

PROBLEM4: problem_example_3_case_1__BBB
Minimize PV (minimize PV of expected spread payments over all periods for tranche m)
subject to
Prmulti_pen ≤ Const5 (risk constraint assuring rating of a tranche)
Box constraints (box constraints on attachment points)
——————————————————————–
PV = Present Value
Prmulti_pen = Probability Exceeding Penalty for Loss Multiple
Box constraints = constraints on individual decision variables
——————————————————————–

Dataset1 5 10,000 0.583782987354 0.35 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 5 500,000 0.587443654069 102.60
NOTE: Problem statements can be simplified using InnerProduct and a set of matriсes.

PROBLEM5: problem_example_3_case_2__BBB
Minimize PV (minimize PV of expected spread payments over all periods for tranche m)
subject to
Linearmulti = Const6 (linear constraints)
Prmulti_pen ≤ Const7 (risk constraint assuring rating of a tranche)
Box constraints (box constraints on attachment points)
——————————————————————–
PV = Present Value
Linearmulti = Linear Multiple
Prmulti_pen = Probability Exceeding Penalty for Loss Multiple
Box constraints = constraints on individual decision variables
——————————————————————–

Dataset1 5 10,000 0.781881852210 0.18 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 5 500,000 0.0.777903066508 1.46
NOTE: Problem statements can be simplified using InnerProduct and a set of matriсes.

PROBLEM6: problem_example_4_case_1__BBB
Minimize Linear (minimize upper bound of spread payments over all periods for tranche m)
subject to
Prmulti_pen ≤ Const8 (risk constraint assuring rating of a tranche)
Linear ≥ Const8 (constraint on income spread payments)
Linear = 1 (sum of weights constraint)
Box constraints (box constraints on attachment points)
——————————————————————–
Prmulti_pen = Probability Exceeding Penalty for Loss Multiple
Box constraints = constraints on individual decision variables
——————————————————————–

Dataset1 58 10,000 1.005085900229 6.37 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data