A reputation strategic model of monetary policy in continuous-time

This paper develops a reputation strategic model of monetary policy with a continuous finite or infinite time horizon. By using the optimal stopping theory and introducing the notions of sequentially weak and strong rational expectation equilibria, we show that the time inconsistency problem may be solved with trigger reputation strategies not only for stochastic but also for non-stochastic settings even with a finite horizon. We show the existence of stationary sequentially strong rational expectation equilibrium under some condition, and there always exists a stationary sequentially weak rational expectation equilibrium. Moreover, we investigate the robustness of the sequentially strong rational expectation equilibrium behavior solution by showing that the imposed assumption is reasonable.