A novel finite-time q-power recurrent neural network and its application to uncertain portfolio model

Abstract

This paper presents a novel finite-time q-power recurrent neural network (FT-QPNN) for uncertain portfolio model. An uncertain mean–variance-skewness model under concave transaction costs is discussed. This portfolio model is essentially a nonconvex nonlinear optimization problem with a non-positive definite Hessian matrix of the Lagrange function. The non-positive definite Hessian matrix leads to the failure of many recurrent neural network methods in solving the problem, and many recurrent neural networks cannot converge to the equilibrium point in finite time. To overcome these difficulties, the FT-QPNN is proposed. Combined with finite-time activation function and local convexification method, the FT-QPNN can solve the optimization problem with non-positive definite Hessian matrix and converge to the equilibrium point in finite time. The global finite-time stability and robustness properties of the FT-QPNN are proved theoretically and verified by numerical experiments. Furthermore, the proposed FT-QPNN is applied to solve the uncertain portfolio model. The application simulation results and comparative experiments with other methods respectively illustrate the feasibility and superiority of the FT-QPNN.