Decision making under uncertainties is a real and challenging problem to portfolio managers in the banking industry. In this paper, the optimal portfolio choice problem has been modelled by the non linear expectation method. The mathematical modelling process shows an optimal problem when the objective function is he expectation of the utility function of the terminal wealth, the state function is the differential equation of the total asset portfolio, and the equality constraints are the

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... l proportions and the capacity. This problem has been numerically solved by using the discretization of the fourth order Runge Kutta method because of its strong numerical convergence and easiest implementation by python programming language. The obtained optimal results show the dynamic of the total asset portfolio, the evolution of the optimal proportions in accordance with the capacity, the dynamic of loans and the market securities. The significant gain control are confirmed.