Costly information transmission in continuous time with implications for credit rating announcements

This paper formulates a continuous-time information transmission model in which an altruistic sender privately observes a stochastic state variable, and incurs a communication cost when she broadcasts a message. We characterize the sender's optimal announcement strategy using an ordinary differential equation. We prove the optimality of the sender's strategies using a martingale verification argument and show that the sender's optimal strategy involves sending discrete messages. Furthermore, we apply the model to the timing decision of credit rating announcements and provide a framework to study various aspects of rating announcements, such as the probability of rating reversals and the expected time before a rating change.