Case study background and problem formulations
Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.
PROBLEM 1: VaR minimization
Miminize Var_risk (minimizing VaR with confidence level alpha)
subject to
Linear ≥ Const (linear constraint)
Box constraints (upper/lower bounds on positions)
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Var_risk = VaR Risk for Loss
Box constraints = constraints on individual decision variables
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Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Miminize Var_risk (minimizing VaR with confidence level alpha)
subject to
Linear ≥ Const (linear constraint)
Box constraints (upper/lower bounds on positions)
——————————————————————–
Var_risk = VaR Risk for Loss
Box constraints = constraints on individual decision variables
——————————————————————–
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 | 23 | 10,000 | -0.001977571995 | 0.11 | |||
---|---|---|---|---|---|---|---|
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 | 23 | 100,000 | -0.002140167562 | 7.49 |
PROBLEM 2: Minimization of Difference of CVaRs
Miminize ((1-alpha_1)/(alpha_2-alpha_1))*CVaR_risk1 – ((1-alpha_2)/(alpha_2-alpha_1))*CVaR_risk2 (minimizing difference of two CVaR functions with confidence levels alpha_1 and alpha_2 satisfying inequalities alpha_1 < alpha < alpha_2)
subject to
Linear ≥ Const (constraint on the portfolio rate of return)
Box constraints (upper/lower bounds on exposures)
——————————————————————–
CVaR_risk = CVaR Risk for Loss
Box constraints = constraints on individual decision variables
——————————————————————–
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
Dataset1 | 23 | 10,000 | -0.001972530367 | 0.01 | |||
---|---|---|---|---|---|---|---|
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 | 23 | 100,000 | -0.002115116297 | 0.07 |
CASE STUDY SUMMARY
Problems 1 minimized VaR using standard PSG risk function VaR_Risk. Let us denote the confidence level of VaR by alpha in Problem 1. Problem 2 minimized the difference of two CVaR functions with confidence levels alpha_1 and alpha_2 satisfying inequalities alpha_1 < alpha < alpha_2. Confidence levels alpha_1 and alpha_2 are close to alpha.