Dynamic risk management of the lending rate policy of an interacted portfolio of loans via an investment strategy into a discrete stochastic framework

Lending rate policy via an appropriate investment strategy for an interacted portfolio of loans into discrete stochastic framework is examined in this paper. A bank optimization model with several control variables, stochastic inputs and a smoothness criterion described by a quadratic functional is proposed for managing the task. The state variable of the system corresponds to the accumulated surplus profit or loss can oscillates deliberately absorbing fluctuations in the different parameters involved. The theoretical model is solved using standard linearization and advanced stochastic optimization techniques resulting in analytic formulae for the control variables. These solutions are actually feedback mechanisms of the past accumulated surplus profit or loss of each sub-portfolio of loans. At the end, a numerical application is presented deriving a smooth solution for the development of the controllers.