No, we don't. A western medieval standard fantasy setting that doesn't include oriental stuff doesn't have a martial unarmed combatant.
The reason for this is that 1) using your hands is dumb when your foes have swords and 2) there are no examples of unarmed combat schools that survive in the west. Sure, there are swordsmanship manuals that have a few elbow and knee techniques that would look familiar to certain Eastern martial artists, but nothing without weapons. Fists were what was used when not even a club or dagger was at hand, and I think that's adequately explained by the standard d3 of damage, assuming it exists in 4E, and what I'm guessing is a lack of any proficiency bonus.
The closest that you get in the west is Greek
pankration, but even that's not going to be terribly useful against a hoplite in full panoply, or a griffon for that matter. IMO, psionics or ki is the only thing that makes an unarmed fighting class even remotely plausible when they're facing down enemies in armor, much less dragons whose scales can scarcely be cut by normal weapons.