Abstarct: In this thesis, a neural network model is presented for solving convex second-order cone programming problems and then to solve portfolio optimization problems in the probability-credibility space. To begin with, in the first chapter reviews the basic mathematical and financial concepts, and in the second chapter fuzzy concepts and credibility theory. in the third chapter, the introduction of recurrent neural networks has been proposed. In the fourth chapter, the optimal conditions for the optimization problem are considered And then a corresponding neural network model is designed. We show that the neural network equilibrium point is equivalent to the optimal solution of the main problem. Also, the proposed neural network model is Lyapunov stable and converges globally to the optimal answer. In the last chapter, by introducing the probability-credibility space, we will solve the portfolio optimization problem by the equilibrium risk value (ERV). The portfolio problem is constructed as a expected value model (EV) of a random fuzzy subject to ERV constraint. It is called the ERV-EV model. The ERV-EV model is a convex programming problem. Computational results show that the equilibrium optimization method is better than the random optimization method in perspective of diversity.