Shane,
We need to simulate problems where human solutions deviate from what is observably optimal. With AI, the program must model both the underlying physics of a problem, and it must model a human response to this physical model.
For both of these models we must decide how much detail to build in.
These models include rules that often resemble or approximate equations from quantum mechanics. A particularly interesting similarity is the statistical nature of Bayesian calculations and the statistical representation of amplitude flows in quantum mechanics.
As Justin said, "I could not absorb that much money intelligently".
I think a chunk of currency on-par with the US GDP is not a liquid asset. If you could accumulate such a sum, introducing it into the market would probably deflate whatever currency it was introduced as. It would be roughly equivalent to minting it fresh.
The smartest thing to start with might be a system of checks and balances for your own spending. You'd look like a government at that size, so it's probably best to behave like responsible one.