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This article deals with the starting and stopping problem under Knightianuncertainty, i.e., roughly speaking, when the probability under which thefuture evolves is not exactly known. We show that the lower price of a plantsubmitted to the decisions of starting and stopping is given by a solution of asystem of two reflected backward stochastic differential equations (BSDEs forshort). We solve this latter system and we give the expression of the optimalstrategy. Further we consider a more general system of $m$ ($m\geq 2$)reflected BSDEs with interconnected obstacles. Once more we show existence anduniqueness of the solution of that system.

The Starting and Stopping Problem under Knightian Uncertainty and Related Systems of Reflected BSDEs