Reserach On Loan Portfolio Optimization Decision Based On Fuzzy Numbers Theory

The loan resource of commercial bank is the main method to solve the capital problem for current economic enviroment. So the optimization of loan portfolio is very important for each commercial bank to realize the credit gains and risk management. In 1952, Markowitz had given the fundamental theory and research approach for security market. In particular, China’s financial markets are in development and improvement phase, commercial banking information system are gradually built up, due to the randomness of events and presence of vagueness that changes in various factors affecting the market, there are still inadequate historical data can be used to effectively estimate future lending rates. Moreover, as China’s market-oriented interest rate process, the magnitude of possible changes in interest rates will be even greater. Under the new Basel Capital Accord, the commercial banks’requirements for risk management and control become more stringent, uncertainties loan yields also showing different characteristics, which put forward higher requirements for a reasonable allocation of resources to commercial banks.The topic is mainly based on the background of the New Basel Capital Accord. Combined with the modern portfolio theory, loan portfolio, risk adjusted return on capital index and economic capital management index, this paper builds the loan portfolio optimization model and analyzes decision-making behavior of commercial banks loan portfolio with the uncertainty of the environment through mathematical programming, optimization theory and fuzzy mathematics method and other tools. The results can improve the loan portfolio optimization model and portfolio theory, and guide commercial banks to optimize the management and its credit operations.The main results are in the following:1. Establish loan portfolio optimization model combined with risk-return mechanism conditions and economic capital constraints. When portraying loan yields combined triangular fuzzy numbers, the loan portfolio optimization model based on risk-adjusted capital return are built, which meets the commercial banks strategic objectives of maximizing the overall risk-return, to a more practical and broad ideas for model building and solving, using a more practical and broad ideas to build and solve model. Moreover, comparatively analyze the specific performance of three loan portfolio model to guide commercial banks to optimize the management of credit operations, enhance its internal fine management level.2. Construction of the loan portfolio optimization model based on three types of fuzzy numbers of LR. According to a commercial bank credit customer data, and comparative analysis of the loan portfolio optimization decisions under three LR type fuzzy numbers, getting the loans optimal distribution ratio of overall comprehensive income RAROC maximization, which reveals relevant parameter changes affect the loan allocation of resources and what fuzzy numbers using the current loan portfolio of commercial banks can bring more reasonable and advantages.3. Construction of interval fuzzy numbers loan portfolio optimization model. Construction of the loan portfolio optimization model will be under interval fuzzy number and through de-compositing the combination variance into systematic risk and non-systematic risk variance constraints to simplify and solve the transformed loan portfolio model. Meanwhile, this paper uses commercial banks own subjective needs to set the relevant parameters, analyzes the optimal resources allocation under different lending credibility to provide commercial bank some suggests with the actual management of lending resources.