There's no right answer to your question. The author doesn't say whether he does or not; she intentionally leaves it unclear so that you need to decide for yourself. What's your gut answer? If you think he lives, then write your paper about why he lives. Same for if you think he dies. I'd like to think that he lives, but that's just me; I like happy endings. How
you answer says more about you than it does about the book itself. Maybe you should write your paper on that thought — how personal interpretation plays into literature.