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_1
Maximize Exp_eut (maximizing Exponential Utility)
subject to
Linear = Const (budget constraint)
Box constraints (bounds on positions)
——————————————————————–
Exp_eut = xponential Utility
Box constraints = constraints on individual decision variables
——————————————————————–Data and solution in Run-File Environment
Maximize Exp_eut (maximizing Exponential Utility)
subject to
Linear = Const (budget constraint)
Box constraints (bounds on positions)
——————————————————————–
Exp_eut = xponential Utility
Box constraints = constraints on individual decision variables
——————————————————————–
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | Problem Statement | Data | Solution | 12 | 199,554 | -15.030566742946 | 1.56 |
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | Matlab code | Data | Solution | 12 | 199,554 | -15.031 | 0.98 |
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | R code | Data | 12 | 199,554 | -15.031 | 0.98 |
PROBLEM 2: problem_2
Maximize Linear-Quadratic Utility
subject to
Linear = Const (budget constraint)
Box constraints (bounds on positions)
——————————————————————–
Linear_Quadratic_Utility(Return) = expected value of piecewise linear-quardatic-linear function of Return
Box constraints = constraints on individual decision variables
——————————————————————–
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | Problem Statement | Data | Solution | 12 | 199,554 | 20.033358148852 | 0.17 |
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | Matlab code | Data | Solution | 12 | 199,554 | 20.033358148852 | 0.28 |
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | R code | Data | 12 | 199,554 | 20.033358148852 | 0.28 |
PROBLEM 3: problem_3
Maximize Log_eut (maximizing Logarithmic Utility)
subject to
Linear = Const (budget constraint)
Box constraints (bounds on positions)
——————————————————————–
Log_eut = Logarithmic Utility
Box constraints = constraints on individual decision variables
——————————————————————–
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | Problem Statement | Data | Solution | 12 | 199,554 | 0.224365972673 | 0.18 |
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | Matlab code | Data | Solution | 12 | 199,554 | 0.224365972673 | 0.14 |
Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|
Dataset1 | R code | Data | 12 | 199,554 | 0.224365972673 | 0.14 |
CASE STUDY SUMMARY
Utility functions are quite popular in various financial applications. This case study compares portfolio optimization problems with Exponential, Logarithmic, and Linear-Quadratic utility functions. The rate of return dataset for a portfolio is provided for benchmarking purposes by EpiRisk Research company via Drs. Roger Wets and Michael Tian. The EpiRisk Research relies on letting the manager of a fixed-income portfolio solve a sequence of so-called tacking (optimization) models, described below, to shape the returns’ distribution. The shape of the distribution is adjusted by selecting the coefficients of the appraisal (~ utility) function.
Utility functions are quite popular in various financial applications. This case study compares portfolio optimization problems with Exponential, Logarithmic, and Linear-Quadratic utility functions. The rate of return dataset for a portfolio is provided for benchmarking purposes by EpiRisk Research company via Drs. Roger Wets and Michael Tian. The EpiRisk Research relies on letting the manager of a fixed-income portfolio solve a sequence of so-called tacking (optimization) models, described below, to shape the returns’ distribution. The shape of the distribution is adjusted by selecting the coefficients of the appraisal (~ utility) function.