Risk-based Decisions on the Asset Structure of a Bank under Partial Economic Information

We present a model of a bank's dynamic asset management problem in the case of partially observed future economic conditions and with regulatory requirements governing the level of risk taken. The result is an optimal control problem with a random terminal condition arising from the partial observation of a parameter of a maximized functional. The Stochastic Maximum Principle reduces the problem to finding a solution to a Forward Backward Stochastic Differential Equation (FBSDE). As optimization usually implies the dependence of the forward equation on solutions of the backward equation we allow the drift and diffusion of the forward part to be functions of the solution of the backward equation. The necessary conditions for the existence of solutions of FBSDE in such a form are derived. A numerical scheme is then implemented to solve a particular case.