A Two-Level Loan Portfolio Optimization Model

Loan portfolio optimization is a core of modern commercial bank asset man-agement. With the economic and social development, its importance makes its the focus of attention by commercial banks. In this paper, we study a two-level loan portfolio optimization problem, a problem motivated by our work for some commercial banks in China, from the view of internal structure of commercial banks. 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 first formulate this problem as a two-level port-folio optimization problem which integrates portfolio theory with a gradually prevalent risk measure, Conditional Value-at-Risk(CVaR). Then, we modify the projection algorithm of stochastic approximation methods and propose a Monte Carlo based inaccurate line search with the help of dual solutions of lower prob-lems. We prove that it is a convergent algorithm. After that, we also propose some useful propositions for a better understanding of the model. Numerical re-sults are included to validate the method and to compare our two-level problem with its corresponding one-level problem.