Abstract: As a main source of profits in China's commercial banks, loan business has direct impact on the operating performance of banks. In this paper, we first establish a risk semi-absolute deviation risk interval based on the principle of semi-absolute deviation risk function. Then we produce an interval planning model by taking the loan portfolio risk represented by the interval number as the objective function and the target rate of return expressed by the interval number as the constraint. This model controls the risk of all loan portfolios, including “incremental portfolio and old portfolio” and solves the optimal allocation of loans. Through empirical analysis, it is shown that this model is superior to the existing models of the same nature.
The main contribution of this research liesin three aspects. First, we describe the risk range based on the combined semi-absolute deviation risk function, which reflects the essence of risk. We consider the correlation between multiple loans to remedy the drawback of the existing linear interval algorithm which neglects the correlation between various loans to exaggerate the portfolio risk. Second, the size of the risk is controlled by minimizing the midpoint of semi-absolute deviation interval of the total loan portfolio m(σ^total), and the range of the risk is controlled by minimizing the radius of semi-absolute deviation interval of the total portfolio w(σ^total), and the multi-objective planning model is established to control the size and scope of the total loan risk including “incremental portfolio and old portfolio”. This model solves the problem of the existing interval planning models which ignore controlling the range of risk interval and altering traditional idea that only considers the risk of incremental portfolio and ignore the huge risk of old portfolio. The third is to solve the multi-objective programming model based on fuzzy two-stage algorithm, which solves the problem of uncertain combinatorial coefficient in multi-objective linear weighting.

Key words: old portfolio, incremental loan portfolio, semi-absolute deviation, nonlinear interval number, portfolio optimal model