Even after completely saturating the market, a large asteroid would easily fetch tens of trillions over the next hundred years. The first person to bring in a large metal- and ice-rich asteroid would dominate the space production market for decades to come.
Does it? By "bring in", I assume we are talking about placing into a convenient orbit, because I do not see a reasonable way to bring a large asteroid down to the surface in the forseable future.
However, my (non laywer) understanding of space law is that it is prohibited (by treaty) to own celestial objects. You can own samples you minded from them, but not the objects themselves. If this understanding is correct, it means that after you park the asteroid in orbit, you are allowed to mine it, and sell the ore. However, so is everyone else; despite the fact that you invested the money in moving the asteroid.
When / if we get to mining asteroids, and generally inhabiting space, either personally or via robots, treaties / laws will be remapped to match the reality of the times.
It would probably be based on a homesteading system. In the case of a planet, you'd get what you changed. In the case of an asteroid, if you moved it into a different orbit and set up facilities on it that's probably enough to count as a homestead.
Over 200 asteroids are known to be larger than 100 km,[49] and a survey in the infrared wavelengths has shown that the asteroid belt has 0.7–1.7 million asteroids with a diameter of 1 km or more.[1]
The volume of a sphere 1 kilometre in radius 4.19km³. If you can build a mining operation on one of those I don't see any problem with granting you exclusive access. We already do something similar on Earth.
I mean, even if we got a tenth of that value, it would still be a tremendous amount of money and could spur whole new industries on earth, much like the advent of steel production did.
Doesn't abundance of certain material make it cheaper? So the value isn't necessarily linearly dependent on the amount.
Reminds me "The Laxian Key" by Robert Sheckley[1] (read it, if you haven't yet).
[1]. https://archive.org/stream/galaxymagazine-1954-11/Galaxy_195...