Most translations seem to take the phrase προσθες ημιν πιστιν in the sense of "increase our faith", but the Greek literally says something like "add to us faith" - the pronoun ημιν reflects a dative and not a possessive case.
The more literal Orthodox New Testament translates the phrase "Add faith to us". This particular phrase does not imply, however, that the Apostles were completely devoid of faith to begin with. "They do not ask faith simply, lest thou shouldst imagine them to be without faith," writes Cyril of Alexandria; "but they rather ask of Christ an addition to their faith, and be strengthened therein" (Commentary on the Gospel According to St. Luke, Sermons CXIII-CXVI). In his commentary, Cyril explains that faith arises both from God and within ourselves:
For faith partly depends upon ourselves, and partly is the gift of the
divine grace: for the commencement of it depends upon ourselves, and
to maintain confidence and faith in God with all our power; but the
confirmation and strength necessary for this comes from the divine
grace: for which reason, because all things are possible with God, the
Lord says, that all things are possible unto him that believeth
[Mark 9:23].
The patristic understanding of this verse is further summarized by Theophylact:
The apostles had faith in the Lord. But they became aware of their
weakness, and when they heard the Lord speaking to them about great
matters and about the danger they would encounter from the offenses
and obstacles to come, they asked Him to increase the strength of
their faith so that they could accomplish the virtue of which He had
spoken ...
So that the apostles might have the means with which to withstand
offenses, they approach the Lord and say, Increase our faith [KJV],
meaning, "Make us more complete and sure in our faith." The Lord
shows them that they have asked well and that they ought to have this
sure belief that faith is able to do great things, and He says to
them, "If ye had faith, ye might transplant this sycamine."
Explanation of the Gospel of Luke (tr. Chrysostom Press, 2007), p.222