Paul opens his letter to the Romans by calling himself a slave of Jesus Christ. While some writers will try and romanticize the slavery of the Roman Empire (trying to make it look much nicer than American slavery), all will admit that the owner had absolute rights over the slave. They could rent them out, sell them, even kill them. The slave had no rights but only obligations toward the owner. He was property that lived for one purpose, to serve the owner. The slave had nothing that could be called "mine."
In a world where "I have a right to..." and "I expect ..." have become even commonly heard from the mouths of children. It is one of the true paradoxes of the Christian faith, that the only way we can find true freedom is to hand our lives over completely to God, and like Paul accept the title "Slave of Jesus Christ."