Abstarct: In this thesis, a numerical method baxsed on neural networks is presented to solve a class of the financial optimization problems with transaction costs. To do this, we first write the optimality conditions for the optimization problem. Then we design a neural network model related to it. We prove that the equilibrium point of the neural network is the main optimal solution. By presenting an appropriate Lyapunov function, stability and convergence properties of the proposed neural network one stated. For this purpese some definitions of financial concepts in mathematics and some concepts of optimization are presented, then a novel gradient lased neural network model is presented, in continuation an analytic derivation of admissible efficient frontier with borrowing by a neural network model is studied and in end the admissible portfolio selection problem with transaction costs with a neural network model is cosidered.