# VaR vs Difference of CVaRs Minimization

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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Dataset1 23 10,000 -0.001977571995 0.11 # 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 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
——————————————————————–

Dataset1 23 10,000 -0.001972530367 0.01 # 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