The cardinal differences in the theoretical description of classical and quantum particles, contradictions probabilistic (Copenhagen School) deterministic (De Broglie - Bohm theory) interpretation mechanics, features entangled states are briefly discussed. It is assumed that strange properties pair can be explained by localization particles not 3D physical space, but domain a fractal space aris...

We introduce a new measure for the capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term and short-term memory) and local herding behavior (fractal dimension). The efficiency measure is taken as a distance from an ideal efficient market situation. Methodology is applied to a portfolio of 41 stock indices. We find that the Japanese NI...

This study aims to test the adaptive market hypothesis by using myopic behavior of investors as a new proxy. The data have been taken from New York Stock Exchange December 1994 2020. Following this collection data, companies’ stock prices were distributed into six different portfolios based on size, investment, book-to-market value, and operating profit. Ordinal logistic regression was used cal...

Capturing dynamical patterns of stock prices are major challenges both epistemologically as well as financially [1]. The statistical properties of their (time) variations or fluctuations [1] are now well studied and characterized (with established fractal properties), but are not very useful for studying and anticipating their dynamics in the market. Noting that a single fractal gives essential...

In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular...

We investigate whether fractal markets hypothesis and its focus on liquidity and investment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, fractal markets hypothesis considers financial markets as complex systems consisting of many hete...