# Case Study: Portfolio Optimization with Mixed CVaR and Mixed VaR Profiles

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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.

PROBLEM 1: problem_Mixed_CVaR_Profile
maximize Avg_g (maximizing average expected return of the portfolio)
subject to
mixed CVaR ≤A (constraint on the mixed CVaR for the overall portfolio)
CVaR _k ≤ B_k , k = 1,…,K (constraints on individual risks formulated with CVaR)
max_risk_n ≤ B_n, n=1,…,N (set of constraints on individual risks formulated with Maximum Risk)
Box constraints (lower and upper bounds on variables)
——————————————————————–——————
mixed CVaR = weighted sum of CVaRs with different confidence levels
CVaR_k = CVaR of k-th individual risk (including contributions from various contracts)
max_risk_n = Maximum Risk of n-th individual risk (including contributions from various contracts)
Box constraints = constraints on individual decision variables
——————————————————————–——————

Dataset1 804 5,000 1,294,974,119.20 44.78 # 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

Dataset2 804 10,000 1,295,057,851.40 24.39 # 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

Dataset3 804 100,000 1,243,596,369.11 199.68 # 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

NOTE: Problem statements can be simplified using InnerProduct and MultiConstraints.

PROBLEM 2: problem_Mixed_VaR_Profile
maximize Avg_g (maximizing average expected return of the portfolio)
subject to
mixed VaR ≤A (constraint on the mixed VaR for the overall portfolio)
VaR _k ≤ B_k , k = 1,…,K (constraints on individual risks formulated with VaR)
max_risk_n ≤ B_n, n=1,…,N (set of constraints on individual risks formulated with Maximum Risk)
Box constraints (lower and upper bounds on variables)
——————————————————————–——————
mixed VaR = weighted sum of VaRs with different confidence levels
VaR_k = VaR of k-th individual risk (including contributions from various contracts)
max_risk_n = Maximum Risk of n-th individual risk (including contributions from various contracts)
Box constraints = constraints on individual decision variables
——————————————————————–——————

Dataset1 804 5,000 1,566,047,896.30 246.36 # 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