Re: What do you do when a student is acting rudely in your class.
Sounds like you have an issue with a young individual with an ego problem. Marc and others have giving good advice that in most cases would normally be followed by any dojo with a commitment to serious training - after all, that type of behavior is not tolerated in any teaching environment.
So, if your dojo is serious about its budo, this guy needs to change his behavior or be shown the door. However, if the dojocho is more interested in collecting this guy's dues, you got more problems than you realize; as I think someone already mentioned. Allowing this type of behavior to continue will eventually bring all students down to his level because the serious students will leave and all you will have left (and attract) will be just more students like him.