Continuous-Time Mean-Variance Portfolio Optimization

The Markowitz mean-variance portfolio optimization is widely acclaimed as a very important investment strategy. This repository contains three continuous-time versions of the mean-variance portfolio optimization (MVPO) problem. The first two MVPO problems are defined as time-varying quadratic programming (TVQP) problems, while the third MVPO problem is defined as a time-varying nonlinear programming (TVNLP) problem. The purpose of this package is to solve online the continuous-time versions of the MVPO problem by using a continuous-time neural network (NN) solver. This solver is the zeroing NN (ZNN). The main article used is the following:

• S.D.Mourtas, C.Kasimis, "Exploiting Mean-Variance Portfolio Optimization Problems through Zeroing Neural Networks", 10(17), 3079 (2022)

M-files Description

• Main_CTMVPO.m: the main function and parameters declaration
• MVPO_EX.m: problem setup
• CTMVPO1.m: main procedure for the two TVQP MVPO problems
• CTMVPO2.m: main procedure for the TVNLP MVPO problem
• dataprep.m: expected return and covariance construction
• problem.m: complementary function for the problem setup
• problem2.m: complementary function for the problem setup
• inputs.m: complementary function for the problem setup
• linots.m: function for vectors' linear interpolation
• linotss.m: function for matrices' linear interpolation
• pchinots.m: time-series piecewise cubic Hermite interpolation of vectors-matrices
• pchinotss.m: time-series piecewise cubic Hermite interpolation of structures
• sp.m: the piecewise polynomial of the cubic spline interpolant of vectors-matrices
• splinots.m: time-series cubic spline interpolation of vectors-matrices
• sps.m: the piecewise polynomial of the cubic spline interpolant of structures
• splinotss.m: time-series cubic spline interpolation of structures
• oomega.m: parameter for spliting the observations to the time periods
• ZNN1.m: the ZNN solver for the two TVQP MVPO problems
• ZNN2.m: the ZNN solver for the TVNLP MVPO problem
• nonlcon.m: the function that includes the nonlinear constraint

Installation

• Unzip the file you just downloaded and copy the CTMVPO directory to a location,e.g.,/my-directory/
• Run Matlab/Octave, Go to /my-directory/CTMVPO/ at the command prompt
• run 'Main_CTMVPO' (Matlab/Octave)

Results

After running the Main_CTMVPO.m file, the package outputs are the following:

• The optimal portfolio of the selected CTMVPO problem created by ZNN.
• The time consumptions of ZNN, quadprog and fmincon.
• The graphic illustration of the portfolio weights along with the optimal portfolios expected return, variance and the error between the ZNN, quadprog and fmincon.

Environment

The CTMVPO package has been tested in Matlab 2021a on OS: Windows 10 64-bit.