In this book, we review the foundational mathematical elements used in finance to test the hypothesis of informational efficiency, including time series analysis: from the random walk to the Black Scholes equation, the flagship concept of modern portfolio management and financial markets. The idea behind this in-depth examination of these founding mathematical concepts is to understand where their weaknesses lie and the consequences of their use in the financial market. We then attempt to correct the fundamental basis of these postulates by introducing the quantum formalism which seems to better translate the psycho-mechanical mechanisms of the markets.
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