The books of Luke and Acts are one continous narrative, Acts is essentially volume 2 of the book of Luke. Since the book of Acts ends with Pauls's first stay in prison in Rome, with no date set for his trial, and the persecutions of Christians by Nero (A.D. 64) not having yet taken place, it could not have been written any later than A.D. 63. The abrupt ending indicates that Luke has come to the end of history that he can recount--at the time it was written there was no more to tell.
Encountering the New Testament, Walter A. Elwell / Robert W. Yarbrough, 1998, Baker Books, page 210
A Survey of the New Testament, Third Edition, Robert H. Gundry, 1994, A Survey of the New Testament, Third Edition, Robert H. Gundry, 1994, Zondervan, page 210