you go to the foreign country, you register a company there in their free zone area (tax free status there, and no foreign tax apply). you might pay a small amount like a consumption duty, but they do it like that in some third world countries to attract businesses to locate there and save on taxes, and for them the employment it provides for the local population. That's sort of how it works. All ligit.
Worldwide income must be declared from ALL USA citizens. So if they get any income from that company ...well see the point? Why would anybody making a living trading worry about the low tax rate here in the USA? Just pay them!
But, if your company owned the condo where you live in the offshore country, and owned the car that you use, and paid your restaurant tabs, would uncle sam count that as taxable income.
You are talking about LIVING offshore as opposed to someone living in the states playing games via an offshore vehicle. If you live offshore, your first 70 or 80K of income is tax free. Now if you live offshore and the expenses you claim are legitimate business expenses you could claim them, but as ES states, you can do the same in the states.