The entire notion of identity theft should be inverted. It wasn't your identity that was stolen, it was the money of which ever place didn't verify the person taking the money. So it should be their problem, not your problem.
"Some logged in on the bank website and committed identity theft electronically." "I see, did they take anything else?" "Uh, no." "Oh, good, so all the money's still there?" "What?" It's just my identity that's gone. None of your money?"