I just finished Ruth. In Ruth 4:16, it states, "Then Naomi took the child and laid him in her lap, and became his nurse". There is a footnote in the NASB that says the term, "laid in her lap" is an example of taking "as her own". So, did Naomi or Ruth raise Obed?
It would be both. Since Naomi did not remarry, she would live with Boaz and Ruth the rest of her life. The phrasing means she took an active role in his upbringing.