Optimal Trading Strategies for an Asset with Disordered Return

We explore various trading strategies from a mathematical and practical perspective. Using a geometric Brownian motion with a disorder to model asset price bubbles, we apply this model to multiple periods and explore the trading strategies on real market data (S&P500, NASDAQ and SSE Composite). We nd that the mathematical model is sucessful in predicting large market events such as the 2008 crisis, however fails to generate gains over times of healthy market growth. Three practical models are also presented and show that bene cial trading can be performed using some simple deterministic assumptions. The mathematical and practical methods are compared. i