An investigation of the theory of bank portfolio allocation within a discrete stochastic framework using optimal control techniques

In this paper, it is fully developed a control model considering the evolution of value of bank's Assets. The basic difference equation of the system is designed, including six control variables (three of them determining the mix of investments for bonds, loans and cash, the extra rate of return to customers due to deposits, the rate of capital represents the amount of net equity issuing (i.e. dividends) and the banking cost) and fulfilling a smoothness criterion described by a quadratic functional. The state variable of the system corresponds to the value of bank's Assets can oscillates deliberately absorbing fluctuations in the different parameters involved. The theoretical model is solved using standard linearization and advanced stochastic optimization techniques resulting analytic formulae for the six control variables. These solutions are actually feedback mechanisms of the past value of bank's Assets. At the end, a practical application for the banking system is presented deriving a smooth solution for the development of the six controllers.