Abstract: The unreasonable status that deposit and lending rates are considered as constants in existing literature couldn't immune future interest rate risk, in case deposit and lending rates would be changing. In our assets and liabilities optimization model, we construct the immune constrain of interval interest rate through duration gap of interval numbers of asset and liability, which makes the assets' allocation be immune to interest rate risk with a changing yield of asset and liability. The study shows that interval-biased selection parameter γ of duration gap decides whether the reserved gap makes money or loses money. The result is the interval-biased selection parameter γ of duration gap is 0.5, the absolute value of both ends of gap interval is in minimum; the more γ is greater than 0.5, the larger positive gap is, and more money is earned when interest rate declines;The more γ is less than 0.5, the larger negative gap is, and more money is earned when interest rate rises. The research shows that selection of parameter λ of the length of the interval decides the size of profit or loss and reveals that the chosen of lesser λ can get more risk-based return in positive interest rate management strategy. On the other hand, we set up the function expression of nonlinear interval-based risk portfolio through the semi-absolute deviation of the combination of correlation coefficient, chang the existing studies of linear interval-based algorithm, and simply linear weight the risk of each loan, thereby exaggerate the disadvantages of portfolio credit risk.

Key words: asset-liability management, optimal model, nonlinear interval number, duration, credit risk, semi-absolute deviation