Hello everyone.

I have a problem need to be solved, I do not know which catalog this question belongs to. But let me give an example to demonstrate this:

Letís say there is a stock. When the price is 100, I bought it, I am certain the price will go up, and at some point, I am not that certain anymore, let this point be price at 150. Apparently I have 50% profit at this point. Now, I sensed that, the price might goes down, but eventually it has a probability that go up again like up to 300. About the highest price 300, I do not know the exactly number, but when it goes there, I will know it is the point I sell it. So, here is the interesting thing: when the price goes down, it might go to 140, 130, 120, 110, 100, 90, even 80, I do not know how it goes, but I know, if it goes down to 80, it probably will not go back to 100 again and keep on dropping, thus, I will lose money there of course. One more restrict, once I sell this stock at some point, I can not buy it back. And, at any point higher than 80, the price could go up.

Therefore, if we hold this stock, we might lose money or get the highest profit, if we sell it at some point, it might goes up at that point then we can not make more money or it keeps dropping so we kept what we have at this point.

My question is, purely in Math, what kind of strategy we could use to get more money, and why?

If there is a related book or essay you know, could you tell me please?

Thanks!