Speculating on the stock exchange Imagine you model each stock as a random walk (fractal) and also that you can buy and sell at any price. Suppose also that it 'walks' with the pace of 1.

If you buy, for example, 1000 shares of several companies, for \$100, and you sell every falling position that hits \$95, but keep every company until it reaches \$110. Wouldn't that be a winning strategy?
If by "'walks' with a pace of 1" means that in every time unit there is a 50% chance that the price rises by 1 and a 50% chance that it falls by 1, then this the classic gambler's ruin with a fair coin problem. 

Imagine that for a particular stock you are playing a game where you win $\$1$ or lose $\$1$ with equal probability and that you start with $\$5$ and your opponent starts with $\$10$. If you play until one of you is ruined (i.e., wind up with nothing) then the probability that you will be ruined is $10(5+10)=2/3$ and consequently the probability that your opponent will be ruined is $5/(5+10)=1/3$. This means that your expected winnings will be 
$$
E=\frac{2}{3}(-$5)+\frac{1}{3}($10) = $0
$$
Your expectation is zero and the cost of doing the trades guarantees that you'll lose money in the long run.

The particular numbers are unimportant here: no matter how much money you and your opponent have, the expectation will always be zero if the "coin" is fair.
As a stock investor, I do not think it is possible to model the stock prices. There are systems that work but even then, you may be looking at one good winner to cover 7-8 losers. The problem is that the stock exchange is not logical, it is emotional and all sorts of things, mainly unsubstantiated rumours, have a big instant effect.