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

This article deals with the starting and stopping problem under Knightian uncertainty, i.e., roughly speaking, when the probability under which the future evolves is not exactly known. We show that the lower price of a plant submitted to the decisions of starting and stopping is given by a solution of a system of two reflected backward stochastic differential equations (BSDEs for short). We solve this latter system and we give the expression of the optimal strategy. Further we consider a more general system of $m$ ($m\ge 2$) reflected BSDEs with interconnected obstacles. Once more we show existence and uniqueness of the solution of that system.