Trading and Investment As A Science by Haksun Li

Many people lose money playing the stock market. The strategies they use are nothing but superstitions. There is no scientific reason why, for example, buying on a breakout of the 250-day-moving average, would make money. Trading profits do not come from wishful thinking, ad-hoc decision, gambling, and hearsay, but diligent systematic study.
•        Moving average as a superstitious trading strategy.

2. Many professionals make money playing the stock market. One approach to investment decision or trading strategy is to treat it as a science. Before we make the first trade, we want to know how much money we expect to make. We want to know in what situations the strategy will make (or lose) money and how much.
•        Moving average as a scientific trading strategy

3. There are many mathematical tools and theories that we can use to quantify, analyse, and verify a trading strategy. We will show case some popular ones.
•        Markov chain (a trend-following strategy)
•        Cointegration (a mean-revision strategy)
•        Stochastic differential equations (the best trading strategy, ever!)
•        Extreme value theory (risk management, stop-loss)
•        Monte Carlo simulation (what are the success factors in a trading strategy?)