The time to shut down

At each time, a firm facing uncertainty over future market conditions have to make a decision whether they should continue to produce or stop the process? As the traditional principle, the firm will go out of production when the price of the typical unit does not cover the average variable cost that it must incur to produce the typical unit. In reality the firm can suffer losses today however it can get more gains tomorrow that is enough to make up the losses. It means that this rule seems not be suitable absolutely in an uncertainty environment. And it leads to a rule that the firm only stop producing if average variable costs of unit exceed the price of unit by a positive amount. This paper expects to find this exceeding amount and when a firm will stop producing. Under uncertainty, the price of unit and the average variables cost are assumed to follow a continuous time stochastic process. We wish to apply the optimal stopping time approach in order to solve it.