In this paper we report on a utility function (loss function) and model that we designed by using optimal control theory based on previous studies. we found that: (1) the Hamiltonian multiplier of the bank NPLs growth rate in the model was obtained using the negative derivitive of the utility (defined as loan function minus non-performing loan function) with respect to the NPLs multiplied by a factor which expresses the rate of change in NPLs over time with respect to the NPLs, the formula is λN=(1/δ)(-vmNm-1)=(1/δ)U'; (2) the model determines the equilibrium value of the saddle point of the bank NPLs; (3) the model can explain the NPLS phenomenon in the Chinese banking system as mainly significant in the state owned banks (SOBS); (4) The paper supports the following hypothesis by considering the situation in China: the equilibrium value of the bank NPLs is dependent on micro-economic factors but influenced by macro-economic factors.
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