Supposedly there is a hedge fund making investments entirely automatically:
My point here were more along the line that it doesn’t matter if they have legal rights and obligations if they can hide that they own companies. I also pointed out this was more of a futuristic problem, but it never hurts to solve problems ahead of time.
On the other hand, an AI designed to be profit maximizing may have even less moral than your normal billionaire, and even less worried about repercussions. It may not even care if society collapses and money becomes worthless as long as it has collected all of it.
That is a far cry from running a company. That is using an algorithm as part of your business process. Running the company means deciding who to hire to design, maintain, and update the algorithm, deciding which algorithm to use, and convincing investors that it’s a good idea.