I used to post here back in high school and haven't visited for a long time due to not reading comics that frequently. I have been watching the animated movies as they've come out and adored Batman: Under the Red Hood.
I have to ask, what happened to Jason Todd at the end? Did he die? Is he still about? The conversation between Batman and Alfred didn't seem to answer this.
As far as the movie goes, your guess is as good as anyone else's. I think they left it ambigious on purpose, and no body was found.
In the comics, after the storyline that the movie was based on, Jason is still alive.