https://phys.org/news/2020-03-mathematicians-theory-real-world-randomness.html Brownian motion describes the random movement of particles in fluids, however, this revolutionary model only works when a fluid is static, or at equilibrium. In real-life environments, fluids often contain particles that move by themselves, such as tiny swimming microorganisms. These self-propelled swimmers can cause movement or stirring in the fluid, which drives it away from equilibrium. Experiments have shown that non-moving 'passive' particles can exhibit strange, loopy motions when interacting with 'active' fluids containing swimmers. Such movements do not fit with the conventional particle behaviours described by Brownian motion and so far, scientists have struggled to explain how such large-scale chaotic movements result from microscopic interactions between individual particles. Now researchers from Queen Mary University of London, Tsukuba University, École Polytechnique Fédérale de Lausanne and Imperial College London, have presented a novel theory to explain observed particle movements in these dynamic environments. They suggest the new model could also help make predictions about real-life behaviours in biological systems, such as the foraging patterns of swimming algae or bacteria. Dr. Adrian Baule, Senior Lecturer in Applied Mathematics at Queen Mary University of London, who managed the project, said: "Brownian motion is widely used to describe diffusion throughout physical, chemical and biological sciences; however it can't be used to describe the diffusion of particles in more active systems that we often observe in real life." By explicitly solving the scattering dynamics between the passive particle and active swimmers in the fluid, the researchers were able to derive an effective model for particle motion in 'active' fluids, which accounts for all experimental observations. Their extensive calculation reveals that the effective particle dynamics follow a so-called 'Lévy flight', which is widely used to describe 'extreme' movements in complex systems that are very far from typical behaviour, such as in ecological systems or earthquake dynamics. Dr. Kiyoshi Kanazawa from the University of Tsukuba, and first author of the study, said: "So far there has been no explanation how Lévy flights can actually occur based on microscopic interactions that obey physical laws. Our results show that Lévy flights can arise as a consequence of the hydrodynamic interactions between the active swimmers and the passive particle, which is very surprising." The team found that the density of active swimmers also affected the duration of the Lévy flight regime, suggesting that swimming microorganisms could exploit the Lévy flights of nutrients to determine the best foraging strategies for different environments. Dr. Baule added: "Our results suggest optimal foraging strategies could depend on the density of particles within their environment. For example, at higher densities active searches by the forager could be a more successful approach, whereas at lower densities it might be advantageous for the forager to simply wait for a nutrient to come close as it is dragged by the other swimmers and explores larger regions of space. "However, this work not only sheds light on how swimming microorganisms interact with passive particles, like nutrients or degraded plastic, but reveals more generally how randomness arises in an active non-equilibrium environment. This finding could help us to understand the behaviour of other systems that are driven away from equilibrium, which occur not only in physics and biology, but also in financial markets for example." English botanist Robert Brown first described Brownian motion in 1827, when he observed the random movements displayed by pollen grains when added to water. Decades later the famous physicist Albert Einstein developed the mathematical model to explain this behaviour, and in doing so proved the existence of atoms, laying the foundations for widespread applications in science and beyond.
The ultimate efficiency is the ultimate randomness. Remember that. As time passes financial markets are going to get more and more random and introduce "irrational" behaviour more often (all other things being equal and linearly trending, that is). That's a result of supply side getting ever more stronger and more capitalized to take the other side of your position. He's covered, you're not. Which way you think the markets are gonna go ? Interesting how the general mass thinks that markets are driven by the demand side. It's all about the bid/ask quotes. If those get dropped then the next trade can easily be yours even though it's 500 points below "market"
A few years ago when I tried to understand the behavior of stock prices, I googled Wiki and it said they behaved more like a Levy process than Gaussian. Aren't these guys a little late to the game?
that may be true for extremely short time frames. even for 5 min markets are far from random........it is only necessary to think in a certain way
Soros got it right...he said they were 'inherently unstable' that is quite different from chaotic. You may not be able to predict explain or rationalize Human behavior but that does not mean human behavior is random or chaotic
This new work on particle motion in fluids will not be applicable to financial markets. In my opinion, Pudutrader has it correct. Just read Soros. He understands financial markets correctly. You'll never be perplexed by the behavior of financial markets again. Two of his books I can highly recommend: "The Alchemy of Finance," and "The Soros Lectures at the Central European University." You will discover Soros's explanation for formation of market bubbles fit the observed behavior perfectly. You'll never be suckered by traditional "market equilibrium theory" again.
Yep, Soros is right about reflexivity https://arxiv.org/abs/1302.1405 Critical reflexivity in financial markets: a Hawkes process analysis Stephen J. Hardiman, Nicolas Bercot, Jean-Philippe Bouchaud We model the arrival of mid-price changes in the E-Mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to -1.15 at short times, less than approximately 10^3 seconds, and crosses over to a second power-law regime with a larger decay exponent of approximately -1.45 for longer times scales in the range [10^3, 10^6] seconds. More importantly, we find that the Hawkes kernel integrates to unity independently of the analysed period, from 1998 to 2011. This suggests that markets are and have always been close to criticality, challenging a recent study which indicates that reflexivity (endogeneity) has increased in recent years as a result of increased automation of trading. However, we note that the scale over which market events are correlated has decreased steadily over time with the emergence of higher frequency trading. ..... The study provides a framework for understanding high-frequency activity in financial markets from 1998 to 2011. Two regimes are identified through Detrended Fluctuation Analysis: one at high frequencies with a Hurst exponent (H) of approximately 0.63, and another at much lower frequencies with H ≈ 0.95. The analysis uncovers a power-law decay in the Hawkes kernel, which describes how past events influence future activity, rather than an exponential decay. The branching ratio from calibrating the model to the E-mini S&P over 14 years is near critical and remains constant over time, which contradicts Filimonov & Sornette's claim that reflexivity has increased since 1998. However, the short lag cut-off of the power-law kernel has decreased over time due to the emergence of higher frequency trading and improved temporal resolution in the market. The Hawkes kernel is found to be described by two power-laws: one decaying as ≈ τ^(-1.15) for short time scales (τ < 1000 seconds) and another decaying faster at ≈ τ^(-1.45) for longer time scales. The long-time regime aligns with the slow decay of volatility correlations reported in existing literature. The study concludes that bursts of diverging trading activity are as inevitable now as in 1998, but the time-scale over which they occur has significantly shortened in the last decade. Financial markets seem to be well described by a critical Hawkes process "without ancestors," meaning that the rate of endogenous events is much higher than that of exogenous (news-related) events. While the critical market scenario is believed to be common in most actively traded markets, a detailed explanation for why markets are precisely poised at criticality is still lacking.