Black Swans and fractals: a better way to understand financial markets?

The last decades produced several empirical observations apparently contradicting the main insights of classical finance, suggesting that traditional capital market theory based on the assumptions of rational investors, efficient markets and random walk not always succeeds in properly describing the financial universe. Therefore, the need of a revision of the entire house of modern finance has turned out to be one of the most discussed issues among not only financiers, but also mathematicians and economists.
In such a context, moving from both the powerful instruments and the innovative insights provided by fractal geometry and considering some statistical similarities strictly connecting fractals to financial assets, the goal of my thesis is therefore to propose a possible alternative way to analyse and understand financial markets – that is, the so called hypothesis of fractal markets.
The main milestones of such a revolutionary hypothesis are stable Paretian distribution on the one hand and long-range dependence on the other hand: whereas the former one relates to the peculiar distribution of financial assets returns, thus proposing a specific pattern which differently from the normal distribution contemplates both the leptokurtosis and the heavy tails empirically perceivable in most situations, the latter one refers instead to a peculiar long-term memory effect which biases the way price changes tend to move and fluctuate over time, thus disclaiming the traditional simplifying assumption according to which every event is totally independent of both past and future events. Moreover, such an hypothesis of fractal markets provides a powerful statistical tool, namely the rescaled-range analysis, which can be very helpful to evaluate quantitatively what kind of influence in the financial framework both stable Paretian distribution and long-range dependence actually exercise, manages to explain both the abrupt changes or the discontinuities and the almost-cycles characterising financial assets patterns, associating them to respectively Noah effect and Joseph effect, and includes the concept of multifractal trading time meant as a new dimension, in which the usual clock time can be transformed and from which charts representing financial prices can be generated.
In conclusion, not only having described the main insights proper of the hypothesis of fractal markets from a theoretical point of view, but also having translated them into more practical terms and having carried out some extensive analysis of a few real world situations, what has eventually emerged is that such a way to observe and analyse financial markets, despite not being the absolute Truth, succeeds in offering a much more realistic picture of markets and their risks rather than classical finance and can be therefore considered, answering the question proposed as title of my thesis, Black Swans and fractals: a better way to understand financial markets?, as effectively a better way to understand financial markets.