A two-level loan portfolio optimization problem

In this paper, we study a two-level loan portfolio optimization problem, a problem motivated by our work for some commercial banks in China. In this problem, there are two levels of decisions: at the higher level, the headquarter of the bank needs to decide how to allocate its overall capital among its branches based on its risk preference, and at the lower level, each branch of the bank needs to decide its loan portfolio based on its own risk preference and allocated capital budget. We formulate this problem as a two-level portfolio optimization problem and then propose a Monte Carlo based method to solve it. Numerical results are included to validate the method.