At that time of Trajan's rule, almost all of the de jure territory of the empire was also firmly under Imperial control. The exceptions were the areas of Mesopotamia that Trajan conquered, which were only ever under tenuous control (Hadrian would quickly abandon the territories as being indefensible) and Dacia north of the Danube which was also pretty indefensible, but was kept around because of the precious metal mines found there.

Here's a great map giving an overview of the empire during Hadrian's reign (Hadrian ruled right after Trajan). Most of the threats at this point were external, and the many legions across the borders did a good job of regulating trade and keeping the inside of the empire safe and happily paying taxes. The borders of the empire were situated along large, highly defensible rivers which helped to maintain a firm boundary and helped to minimize any sort of uncontrolled frontier.

One of the reasons that the Romans were able to maintain such a large empire is because they had excellent communication infrastructure: much of their territory was easily accessible by the sea and they had great well-engineered roads, and an Imperial courier service which allowed emperors to quickly receive and dispatch information.