Before revision:  We address this economic question of fiscal stimulus as a new optimal control problem generalizing the model of Dutta and Radner 1999 . We find  that there exists an optimal strategy and provide rigorous verification proof for the optimality .
After revision:  We address this economic question of fiscal stimulus as a new optimal control problem generalizing the model of Dutta and Radner 1999 . We find Shepp (1996). The model allows for the company to borrow continuously from the government. We prove that there exists an optimal strategy and provide rigorous verification proof for the optimality .