The stock market is reactive to who is buying and who is selling. In today's exchanges, prices are modified by the second because of this concept. The price you see on a ticker board is essentially the price of the stock during it's last trade, which effectively becomes the basis for pricing future stock sales.
If there's a huge amount of sellers for stock X and not many buyers, the price tends to go down due to lack of interest. This isn't set by a computer, but rather by the seller, trying to sell off their shares to the "highest bidder", and the way that happens is by lowering your price until someone buys it.
If there's a stock Y that people really want because they support it or it's making good returns (or whatever), then the price people offer for the stocks make the price higher.
Granted, there's some regulation of the prices, but it's mostly about "supply and demand".
"Share prices are set by supply and demand in the market as buyers and sellers place orders. Order flow and bid-ask spreads are often maintained by specialists or market makers to ensure an orderly and fair market."
So what happens when you seriously change the conditions of a stock?
Any change to the supply or demand will cause the price to change. The problem with seeing the future is if the changes the pregoc makes actually increase, decrease, or cause the expected market value of a stock.
For example: if a precog sees a 20% increase in a stock in one day and they buy 10k shares, are they the one that caused the price increase? Does the stock value instead go up by 30%? Does the price instead drop by 10%, because everyone is now trying to sell due to the massive purchase? And can your precog see the change in time to change their purchase from 10k shares up to 15k or down to 2k, depending on the desired outcome? How far in the future can the see? Is it just a few seconds, minutes, days, weeks? And does that change per person, and is variable based on skill or static based on natural talent?
A massive change to a stocks value or trade volume can cause other people to take notice. If enough people, or a large individual investor, follow along with the new trend, it can also affect the valuation of the stock, positively or negatively. This happens without precognition and is called a "run". Either people are running to the stock or away from it. If the run is bad enough, the people monitoring the exchange can cease trading that stock to prevent serious market problems. These problems can kill a company if they are serious enough. They can also seriously affect the future of the stock even after the run ends.
So what happens when you have someone who can predict the future?
There's a couple things that can happen.
A careful/moral investor will make sure their decisions don't seriously affect the expected price by their interest in that stock. They will purchase and sell modest amounts of stock, maybe through intermediaries, and try to prevent runs that cause havoc. They notice an expected rise or fall in prices and invest accordingly.
An immoral investor will try to game the system. They will purposefully cause the stock to be noticed and try to get the price to rise unnaturally, then sell before trading stops or the price takes a nose dive. They will notice a natural rise or fall in prices, then make massive purchases or sales in an effort to make it more drastic and to their advantage.
A newbie may unintentionally cause stock prices to unnaturally rise and fall, but will simply be inexperienced on how to prevent this. They may lose as much money as they earn. They may also lose considerably more than they earn, simply by not paying attention.
Then again, that I've explained happens in today's market. The only difference is that we currently work on historical trends instead of future/expected trends.
There's a problem... and complications...
Unless your Universe is pre-destined to everything, then current decisions affect the future. If you've ever seen the movie "Next" with Nicholas Cage, you'll know that a precog might be able to "try" different things to cause an expected outcome.
In the movie, Cage is able to project himself into the future a variable amount of time, seeing what happens, then changing how he progresses. This is useful to him as he can now predict when and where he is shot, in one scene, so he can effectively dodge the bullets before they are fired. It may not be the best movie around, but it does make you think about how effective being able to see into the future may be, or not, depending on your intelligence.
Are your precogs able to "see" the changes they make in the timeline in "realtime" or are they effectively as blind as anyone else to their purchases and sales. If they see a price go up or down and they make a significant purchase or sale, does that price they see match the price at the time actually forecast? Asked differently: if they look again, does their "vision" change? Can they even look again or is that same instant in time blocked from them somehow? Is it only a function of energy whether they can look forward and how long is their recharge time? This kind of meshes with how far into the future they can see, because if their cooldown is longer than their pre-vision, they might not be able to change their decision anyway, unless there's partners or a team making sure the decisions are correct.
So, does your stock purchase change the future? Can you "ride the wave" of someone else's run and get out before you get stuck? Or does one of your characters realize that precog doesn't change anything and therefore doesn't really matter (pre-destiny)? Maybe there's another set of precogs that work to prevent runs on stocks and effectively "normalizes" the market? Maybe the market is regulated so that only a certain amount/type/size of unnatural market fluctuation are made before a specific individual is required to get more education or is outright banned.
This is your story, so you have to decide what what you want to happen. If you want to make the stock so dangerous that only a fool or genius would participate, you can do that. If you want it to be so regulated that only "masters" allowed to use real money, with everyone else being on a virtual market until they become "certified", you can do that, too. Maybe the stock market was so volatile that it crashed years ago, and no there's only stories/myths about it and how people went mad trying to use it.
Hopefully I provided more insight than questions. "Have fun storming the castle!"