Theoretical study of technical analysis indicators.

Summary In the context of my thesis, I was interested in the mathematical analysis of a volatility breakout indicator widely used by practitioners in the trading room. The Bollinger Bands indicator belongs to the family of so-called technical analysis methods and is therefore based exclusively on the recent history of the price considered and a principle deduced from past market observations, independently of any mathematical model. My work consists in studying the performance of this indicator in a universe that would be governed by stochastic differential equations (Black-Scholes) whose diffusion coefficient changes its value at an unknown and unobservable random time, for a practitioner wishing to maximize an objective function (for example, a certain expected utility of the portfolio value at a certain maturity).