Before revision:  In the case the insider does not know this random time, we see that there is  no full efficiency, but there is nevertheless an equilibrium where the sensitivity of prices is decreasing in time according with the probability that the announcement time is greater than the current time.
After revision:  In the case the insider does not know this random time, we see that there is an equilibrium with no full efficiency, but there is nevertheless an equilibrium where the sensitivity of prices is decreasing in time according with the probability that the announcement time is greater than the current time.