The Study Of Loan Portfolio Optimization Model And Solution

The thesis introduces and analyzes five loan portfolio optimization models atfirst. These models have the same character: establishing on the basis of Markowitzstandard model. But there are different methods of deciding input variables in themodels. Morgan and Gollinger's loan portfolio standard model uses enterprise's ZETAscores as the input variables. The input variables of Altman's loan portfoliooptimization model are derived from expected return, which is decided by Altmanhimself. In KMV loan portfolio management model, the input variables are decidedby expected default frequency that is derived from Option Pricing Model.Decision-making model of loan portfolio optimization based on the yield of VaR onlyintroduces a constraint condition about VaR into the Markowitz standard model.0-1-integer programming model for choosing enterprises decides the input variablesbased on the index of Net Present Value, and changes the standard model into integerprogramming model.All of the models above-mentioned consider the loan portfolio problem from onelevel and do not combine with the layered management of bank. The solving difficultywill increase when the number of loans becomes large. Therefore, A bilevelprogramming model for the loan portfolio optimization problem is established in thethesis. The input variables are worked out from enterprise's credit ratings andtransition matrix of credit rating. At first, the whole loan portfolio of bank is separatedinto several sub-portfolios on the basis of trade. Then the optimization problem whichdecides optimal loan' proportion in every trade is solved by the standard Markowitzmodel at the upper level. At the same time, the 0-1-integer programming models at thelower level are used to determine optimal portfolio of enterprises in each trade. Thismethod can help the bank to control the risk on each level, and rationally decomposethe large-scale loan portfolio problem.For this model that has one optimization problem at the upper level and severaloptimization sub-problems at the lower level, a hierarchical optimization method isproposed. This is a novel method for solving nonlinear bilevel programming problems.By introducing a decoupling vector, a bilevel programming problem is decomposedinto independent optimization sub-problems, which are easily solved at Level 1 of atwo-level hierarchical structure. At Level 2 the decoupling vector is then updatedusing solutions from Level 1. Based on decomposition-coordination principle, theproposed method can finally solve the bilevel programming problem in an iterativefashion. For bilevel programming model of loan portfolio optimization with integers,continualization technique is employed and continualized problems are then equallywell solved using the proposed method. Numerical examples are used to demonstratesimplicity and effectiveness of the method proposed.