There is no word our in the Greek
Thus Barnes notes
The author and finisher of our faith. The word “our” is not in the original here, and obscures the sense. The meaning is, he is the first and the last as an example of faith or of confidence in God—occupying in this, as in all other things, the pre-eminence, and being the most complete model that can be placed before us. The apostle had not enumerated him among those who had been distinguished for their faith, but he now refers to him as above them all; as a case that deserved to stand by itself. It is probable that there is a continuance here of the allusion to the Grecian games which the apostle had commenced in the previous verse. The word author—ἀρχηγὸν—(marg. beginner)—means properly the source, or cause of anything; or one who makes a beginning. It is rendered in Acts 3:15, 5:31, Prince; in Heb. 2:10, Captain; and in the place before us, Author. It does not elsewhere occur in the New Testament. The phrase “the beginner of faith,” or the leader on of faith, would express the idea. He is at the head of all those who have furnished an example of confidence in God, for he was himself the most illustrious instance of it. The expression, then, does not mean properly that he produces faith in us, or that we believe because he causes us to believe—whatever may be the truth about that—but that he stands at the head as the most eminent example that can be referred to on the subject of faith. We are exhorted to look to him, as if at the Grecian games there was one who stood before the racer who had previously carried away every palm of victory; who had always been triumphant, and with whom there was no one who could be compared. The word finisher—τελειωτὴν—corresponds in meaning with the word author. It means that he is the completer as well as the beginner; the last as well as the first
Albert Barnes, Notes on the New Testament: Hebrews (ed. Robert Frew; London: Blackie & Son, 1884–1885), 291–292.
