When I was first driving, I couldn't remember which insurance company I had T_T
I know a situation where a guy caused a friend of mine to crash into a median (didn't stop for a stopsign and made him swerve) and the guy ended up paying for repairs out of pocket just because he was a good person.
I also know a lot of people who would run.
Get a police report, though it's sad to hear an accident will be placed on the car's record. personally, at only 400 bucks, I'd avoid dealing with insurance, and just call the kid and get a written contract notarized that he agreed to pay so much over some period of time, signed by you both. if he runs, you have a legal contract that would enable the police to hunt his ass down.
But that's just me, I hate minor **** going on a car's record.