Risk-based decisions on assets structure of a bank — partially observed economic conditions

A model of bank’s dynamic asset management problem in case of partially observed future economic conditions and requirements concerning level of risk taken has been built. It requires solving the resulting optimal control with random terminal condition resulting from partial observation of parameter of maximized functional. Stochastic Maximum Principle reduces the problem to solving FBSDE. As optimization may usually imply dependence of forward equation on solutions of backward equation we allow the drift and diffusion of forward part to be functions of solution of backward equation. The necessary conditions for existence of solutions of FBSDE in such a form have been derived. A numerical scheme is then implemented for a particular choice of parameters of the problem.