My current location has unreliable internet and electricity.
If you look around on this forum at the complaints against LP, I'm not sure they're a great improvement in connectivity and availability. I think you would be penny wise and pound foolish to put such a high-stakes mission-critical application in an LP datacenter -- they just don't seem to fully have it together yet. I'm assuming that even dedicated servers would suffer from the same power and net problems (e.g., frequent DoS attacks) as do the shared servers. If you're doing forex and stock trading, I think enough money is involved that you should search for a more reliable (and expensive) host, or even build your own datacenter. Security is not going to be as much of a worry if your systems are down or your members can't get through.
As for security itself, any time you turn over your physical machines to another company, you risk their being able to snoop on your customers and trades. I would presume that LP is as ethical as any other general purpose hosting service, but at some point in the process (in the server), your data needs to be in the clear. If you're that concerned about it, you need to build and run the datacenter yourself, with custom-built physical and electronic security systems and a staff that you've checked out.
