Exploiting Mean-Variance Portfolio Optimization Problems through Zeroing Neural Networks

Abstract

In this research, three different time-varying mean-variance portfolio optimization (MVPO) problems are addressed using the zeroing neural network (ZNN) approach. 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. Then, utilizing real-world datasets, the time-varying MVPO problems are addressed by this alternative neural network (NN) solver and conventional MATLAB solvers, and their performances are compared in three various portfolio configurations. The results of the experiments show that the ZNN approach is a magnificent alternative to the conventional methods. To publicize and explore the findings of this study, a MATLAB repository has been established and is freely available on GitHub for any user who is interested.

Towards Higher-Order Zeroing Neural Networks for Calculating Quaternion Matrix Inverse with Application to Robotic Motion Tracking

“…The suggested HZNN model to be utilized when addressing the TVQ-INV of (8) under complex representation of the input TVQ matrix Ã(t) is the dynamic model of (40), denoted by the notation HZNNQC p .…”

“…Let Ǎ(t) ∈ C 2n×2n be differentiable. At each time t, the HZNNQC p model (40) exponentially converges to the THESO k(t) for any possible starting point k(0).…”

“…Particularly, the HZNNQ p model performs 4n 2 additions/subtractions and (4n 2 ) 2 multiplications in each iteration of (23), which results in a computational complexity of O((4n 2 ) 3 ) when an ode MATLAB solver is used. In the same manner, the HZNNQC p model performs 4n 2 additions/subtractions and (4n 2 ) 2 multiplications in each iteration of (40). By converting these measurements from the complex domain into the real domain, the HZNNQC p model performs 8n 2 additions/subtractions and (8n 2 ) 2 multiplications, which results in a computational complexity of O((8n 2 ) 3 ).…”

“…Today their use has expanded to include the resolution of generalized inversion issues, including time-varying Drazin inverse [33], time-varying ML-weighted pseudoinverse [34], time-varying outer inverse [35], time-varying pseudoinverse [36], and core and core-EP inverse [37]. Their use has expanded to include the resolution of linear programming tasks [38], quadratic programming tasks [39,40], systems of nonlinear equations [41,42], and systems of linear equations [43,44]. The creation of a ZNN model typically involves two fundamental steps.…”

Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control

“…Dynamical systems for computing time-varying pseudoinverses were among their subsequent applications [34,35]. Nonlinear equation systems [36,37], linear equation systems [38,39], linear/quadratic programming [40][41][42], and generalized inversion [43,44] are among the challenges that they are currently utilized for. A ZNN model is typically constructed via two primary steps.…”