Can you start your own finance company? Can a PhD good enough to generate these models start his or her own hedge fund without a hundred million dollars?
You can use your models to trade your own funds (that's what Simons -- the guy behind Renaissance -- did), but it's probably not worth it. Imagine that you're good enough to beat the market by 500 basis points: you earn 15% per year when the market does 10. Investing your own retirement funds, and starting at 100K, you'll end up just about doubling your money in five years.
Hedge funds typically charge 20% of profits and 2% of assets. Let's say you spend your $100K paying a lawyer to incorporate you, and you take a year off to raise your first $5 million. Over the next four years, your earnings would start at $250K for year two, and hit $332K by year five. Even accounting for the missed year, the earnings from starting a hedge fund would be an order of magnitude higher than those from running your own money.
This is obviously simplified (I'm ignoring taxes and inflation, which if nothing else will get me dirty looks from my fellow libertarians), but it should illustrate why so many PhDs are getting rich running money for second-generation MBAs.
It is trivially easy to start your own hedge fund. I've got a friend from college that's done it, and obviously my employer's customers have all done it (I work for a financial software startup). All you have to do is file for a LLC - it costs like $45.
The tricky part is a.) finding investors to give you money and b.) investing that money well. Your limited partners have to be "accredited investors", which means they need income of over $200K for the last 2 years or a net worth over $1M. Obviously, it takes a fair amount of persuasion to convince someone to fork over a million dollars. But if you've got a Ph.D in physics or successful experience on Wall Street, it's not all that hard.
A surprisingly common answer to (a) is to just kind of casually ignore those rules for a while. Nobody recommends this, but Warren Buffett, Michael Milken, and James Cramer all admitted to doing it -- and it definitely worked out for them in the end. The spirit of the accredited investor law is to protect the ignorant from the malicious; in the case of smart people willing to risk small sums on other smart people, it doesn't quite apply.