Abstarct: In this thesis, a numerical method baxsed on neural networks is presented to solve the optimization problems in financial mathematics. To do this, we first write the optimization conditions for the optimization problem. Then we design a neural network with it. We prove that the trust point of the corresponding neural network is the main optimal answer. Prove the basis and global convergence of the proposed model by presenting an appropriate Lipanov function. the first, definitions of financial concepts in mathematics and preparatory optimization and neural networks are presented. In the following provide a neural network approach for solving linear programming problems for selecting optimal portfolio with transaction costs And finally, we present an accurate method for solving portfolio optimization problems under random constraints.