You are allowed to be an employee on the payroll of your own company. Getting a 1099 already establishes a trader/investor as self employed, which can be wrapped up in the mighty I.R.S tax benefits of incorporation.
A follow-up question: is it perfectly legal for one person to trade simultaneously through 1) an individual account and 2) a business account with the same broker? Reason for asking this is that in many countries, long-term investment returns are not taxed or the tax is low, whereas short-term trading profits are taxed heavily. So the optimal thing to do would be to handle your long-term investments as an individual and do short-term trading as a business entity. Does anyone know whether this is common or if there are any potential legal obstacles? Do brokers allow this?
I had a company for 4 years that was solely trading my own money. This was stated in the articles of association when the company was founded. I never paid professional fees. Had no problem to find a broker for trading US markets. My broker needed however a copy of the articles of association when the company was founded to be sure I was only trading my own money. I also was the sole managing director of the company. Taxation was much lower. Moved after that to a low tax country and closed the company as I didn't need that construction anymore. I have a Series 7 license, but it was never asked. If I would have traded other people's money too, I would have to obtain a license in the country where I had my company. There are specific rules for trading other people's money in the US. Ask Robert Morse maybe. Not true, I never paid double. In some countries there are ways to avoid this double taxation. Find a good tax consultant.