Research of the Optimal Timing in Banks＇ Write-off Decision Under the Uncertain Conditions

On the assumption that the callback rate of the disposal of NPLs follow GBM, the paper obtains the partial differential equation, which is consistent with the value of waiting for the Non-performing loans disposal, by the method of the stochastic dynamic programming. Then, the equation solution is obtained on the value-matching and smooth-pasting. We can find the optimal timing of the Non-performing-loans disposal and the condition for deferring the Non-performing-loans disposal from the obtained solution.