
If you want to do this to make an income for the stock project team, you could setup fees. Say, a one time fee to be allowed to participate (kind of like the $10.00 thing to register for SL in 1.2, only in Lindens obviously). That could be as simple as selling some kind of stock exchange "device" that allows someone to communicate with the main stock exchange database/objects.
Second, you could sell additional "fake money" credits for small amounts of L$...but be careful if you do this, because if the data is lost due to some kind of server crash/script crash/etc, people will lose their virtual investments. Not sure if there's really a solution for this (this may be a problem if you stick to your original idea, too.) Maybe just sell a stock interface device (a computer, PDA, or whatever) since that can't be lost, and then do the rest of the project just for fun (this would be my preference).
It doesn't need to be all fake companies either... you could use either these or combinations of these:
1) Real life companies and real stock prices
2) Fake companies, perhaps base them on the movements of some real life companies (keeping the identities secret)
3) Entirely fictional companies, create events and basically run it like you're a GM/DM in a roleplaying game (this is like Julian mentioned above, mergers, scandals, etc)
4) SL businesses, if you can figure out some kind of system that can simulate stock prices based on what the SL business is "worth" and ingame sales
Oh, and as for "winning": Ezhar's Senso game can't be "won" (unless you count being on the top of the high score list winning...btw, I am on the top

Operating it as more than a game and trying to mimic a real stock market (in the original way you've suggested) just seems like it's way too complicated to actually make any L$ on. That's my opinion, anyway.
I don't think you're going to get Linden support without either a BIG group of people who are very interested, or having it 90% completed and working. Nothing stopping you from trying though. The SL University project (which may still be active) had a HUGE list of people interested and to my knowledge it didn't get any sort of Linden support...