I'll tell you one thing: Alice better watch herself when dealing with Jack Buyer. That dude kicks terrorist ass and can go a full 24 hours without peeing, sleeping, pooping, or eating. Come to think of it, nobody observed him eat a single bite of food for a full 6 years. This leads some to believe that he a cybergenetic human that doesn't need sleep and excretes waste through a simulated sweating process. Also, sometimes he can teleport himself to places so long as nobody is really paying attention. His dad was pretty badass too, having once fought body-snatching aliens. I guess it runs in the family.
Or it could be that he's actually Doctor Who and, in times of trouble, he time-travels and swaps places with his former or future self so that he can take a nap, replenish his ammo, and get a taco to eat. In that case, Alice can just tell him to hop into the TARDIS, go back a few hours and initiate the transfer, and then come back to the present. Then, he can take Alice a day or so into the future, look up the exchange rate on his smartphone, and go back to the present. That way, they won't have issues with a volatile exchange rate.
Heck, he could set up a miner in a bunker somewhere, go forward several decades, put the now-full wallet on a flash drive, and take it back to the present. Sure, this might introduce a block chain paradox, but since when did Doctor Who give two shits about paradoxes?