A One-Layer Recurrent Neural Network for Real-Time Portfolio Optimization With Probability Criterion

This paper presents a decision-making model described by a recurrent neural network for dynamic portfolio optimization. The portfolio-optimization problem is first converted into a constrained fractional programming problem. Since the objective function in the programming problem is not convex, the traditional optimization techniques are no longer applicable for solving this problem. Fortunately, the objective function in the fractional programming is pseudoconvex on the feasible region. It leads to a one-layer recurrent neural network modeled by means of a discontinuous dynamic system. To ensure the optimal solutions for portfolio optimization, the convergence of the proposed neural network is analyzed and proved. In fact, the neural network guarantees to get the optimal solutions for portfolio-investment advice if some mild conditions are satisfied. A numerical example with simulation results substantiates the effectiveness and illustrates the characteristics of the proposed neural network.

[1]  Liang Jian.  Probability Criterion in Portfolio Investment Model with Commissions , 2001 .

[2]  Mauro Forti,et al.  Convergence of Neural Networks for Programming Problems via a Nonsmooth Łojasiewicz Inequality , 2006, IEEE Transactions on Neural Networks.

[3]  Kin Keung Lai,et al.  A model for portfolio selection with order of expected returns , 2000, Comput. Oper. Res..

[4]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[5]  Jun Wang.  Analysis and design of a recurrent neural network for linear programming , 1993 .

[6]  M. Forti,et al.  Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations , 2006 .

[7]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[8]  Wei Bian,et al.  Subgradient-Based Neural Networks for Nonsmooth Nonconvex Optimization Problems , 2009, IEEE Transactions on Neural Networks.

[9]  Zhigang Zeng,et al.  Associative memories based on continuous-time cellular neural networks designed using space-invariant cloning templates , 2009, Neural Networks.

[10]  Jinde Cao,et al.  A Recurrent Neural Network Based on Projection Operator for Extended General Variational Inequalities , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Shingo Mabu,et al.  A model of portfolio optimization using time adapting genetic network programming , 2010, Comput. Oper. Res..

[12]  Xiaolin Hu,et al.  A Recurrent Neural Network for Solving a Class of General Variational Inequalities , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Xing-Bao Gao,et al.  A novel neural network for nonlinear convex programming , 2004, IEEE Trans. Neural Networks.

[14]  Liu Baodin.  PROBABILITY CRITERION IN INVENTORY SYSTEMS , 1993 .

[15]  Jun Wang,et al.  A dual neural network for kinematic control of redundant robot manipulators , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[16]  Youshen Xia,et al.  A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[17]  André F. Perold,et al.  Large-Scale Portfolio Optimization , 1984 .

[18]  J. Aubin,et al.  Differential inclusions set-valued maps and viability theory , 1984 .

[19]  Jun Wang,et al.  A One-Layer Recurrent Neural Network for Constrained Nonsmooth Optimization , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Youshen Xia,et al.  A new neural network for solving linear and quadratic programming problems , 1996, IEEE Trans. Neural Networks.

[21]  Wansheng Tang,et al.  Fractional programming model for portfolio with probability criterion , 2002, IEEE International Conference on Systems, Man and Cybernetics.

[22]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[23]  Zhigang Zeng,et al.  Design and Analysis of High-Capacity Associative Memories Based on a Class of Discrete-Time Recurrent Neural Networks , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  Jun Wang,et al.  A projection neural network and its application to constrained optimization problems , 2002 .

[25]  Xiaolin Hu,et al.  A Gaussian Attractor Network for Memory and Recognition with Experience-Dependent Learning , 2010, Neural Computation.

[26]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[27]  Mauro Forti,et al.  Generalized neural network for nonsmooth nonlinear programming problems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Qingshan Liu,et al.  A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization , 2012, Neural Networks.

[29]  M. Padberg,et al.  Simple Criteria for Optimal Portfolio Selection , 1976 .

[30]  C. Singh.  Optimality conditions in fractional programming , 1981 .

[31]  Tianping Chen,et al.  Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions , 2006, Neural Computation.

[32]  Abdesselam Bouzerdoum,et al.  Neural network for quadratic optimization with bound constraints , 1993, IEEE Trans. Neural Networks.

[33]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[34]  Katta G. Murty,et al.  Nonlinear Programming Theory and Algorithms , 2007, Technometrics.

[35]  S. Zionts,et al.  Programming with linear fractional functionals , 1968 .

[36]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network With a Discontinuous Hard-Limiting Activation Function for Quadratic Programming , 2008, IEEE Transactions on Neural Networks.

[37]  Xiaolin Hu,et al.  An Alternative Recurrent Neural Network for Solving Variational Inequalities and Related Optimization Problems , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[38]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network with a Discontinuous Activation Function for Linear Programming , 2008, Neural Computation.

[39]  Jun Wang,et al.  A deterministic annealing neural network for convex programming , 1994, Neural Networks.

[40]  Wei Bian,et al.  Subgradient-Based Neural Networks for Nonsmooth Convex Optimization Problems , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[41]  Michael A. Shanblatt,et al.  Linear and quadratic programming neural network analysis , 1992, IEEE Trans. Neural Networks.