What stops it from going up exponentially forever is that in a finite system with finite resources you cannot get an arbitrarily high hash rate. Moreover, since the exponential is a very rapidly increasing function, resources will be exhausted pretty soon, so it cannot continue for very long.

But this does not mean that when the hash rate starts to stabilize anybody will still be profitable. In fact, there are indications that by the time this happens (in a year or so), everybody will be hashing just to limit their losses and nobody will make any profit. So I am not quite sure about the share price rising...