Abstract: Recovery rate is an important parameter of stock uncertainty. Using the probability of improved recovery rate,the number and extent of adjustment and the new recovery rate,recovery rate uncertainty is described. Then effective recoverable stock is determined. In the end,the model of optimal extraction of exhaustible resources is built by using the theory of optimal control.The expressions of optimal extraction path,shadow prices and exhaustible time are received. The results show that:the higher recovery rate is, the more resources are supplied and the longer service life of mining area is gained. Also the resources can be protected;higher recovery rate need more frequent to adjust. When probability of improved recovery rate is high,less frequency of adjustment is required. And it is proved in theory that the action to increase recovery rate is effective.

Key words: exhaustible resources, recovery rate, effective stock, exhaustible time