The understanding of the emergent behaviour of complex systems is probably one of the most intriguing challenges in modern theoretical physics. In the present Thesis we use novel data analysis techniques and numerical simulations in order to shed some light on the fundamental mechanisms involved in their dynamics. We divide the main core of the research into three parts, each of which address a specific, and formally well defined, issue. In the first part, we study the processes of self - organization and herding in the evolution of the stock market. The data analysis, carried out over the fluctuations of several international indices, shows an avalanche - like dynamics characterized by power laws and indicative of a critical state. Further evidence of criticality relates to the behaviour of the price index itself. In this case we observe a power law decline with superimposed embedded log - periodic oscillations which are possibly due to an intrinsic discrete scale invariance. A stochastic cellular automata, instead, is used to mimic an open stock market and reproduce the herding behaviour responsible for the large fluctuations observed in the price. The results underline the importance of the largest clusters of traders which, alone, can induce a large displacement between demand and supply and lead to a crash. The second part of the Thesis focuses on the role played by the complex network of interactions that is created among the elementary parts of the system itself. We consider, in particular, the influence of the so - called " scale - free " networks, where the distribution of connectivity follows a power law, on the antiferromagnetic Ising model and on a model of stochastic opinion formation. Novel features, not encountered on regular lattices, have been pointed out. In the former case a spin glass transition at low temperatures is present while, in the latter, the turbulent - like behaviour emerging from the model is found to be particularly robust against the indecision of the agents. The last part is left for a numerical investigation of an extremal dynamical model for evolution / extinction of species. We demonstrate how the mutual cooperation between them comes to play a fundamental role in the survival probability : a healthy environment can support even less fitted species. / Thesis (Ph.D.)--School of Chemistry and Physics, 2006.

Over the last few years there has been a surge of activity within the physics community in the emerging field of Econophysics—the study of economic systems from a physicist's perspective. Physicists tend to take a different view than economists and other social scientists, being interested in such topics as phase transitions and fluctuations. In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Fluctuations are driven by a stochastic component in the agents' forecasts. As the scale of the fluctuations is varied a critical phase transition is discovered. Unfortunately, this model is unable to generate realistic market dynamics. The second model discards the requirement of centralized trading. In this case the stochastic driving force is Gaussian-distributed "news events" which are public knowledge. Under variation of the control parameter the model exhibits two phase transitions: both a first- and a second-order (critical). The decentralized model is able to capture many of the interesting properties observed in empirical markets such as fat tails in the distribution of returns, a brief memory in the return series, and long-range correlations in volatility. Significantly, these properties only emerge when the parameters are tuned such that the model spans the critical point. This suggests that real markets may operate at or near a critical point, but is unable to explain why this should be. This remains an interesting open question worth further investigation. One of the main points of the thesis is that these empirical phenomena are not present in the stochastic driving force, but emerge endogenously from interactions between agents. Further, they emerge despite the simplicity of the modeled agents; suggesting complex market dynamics do not arise from the complexity of individual investors but simply from interactions between (even simple) investors. Although the emphasis of this thesis is on the extent to which multi-agent models can produce complex dynamics, some attempt is also made to relate this work with empirical data. Firstly, the trading strategy applied by the agents in the second model is demonstrated to be adequate, if not optimal, and to have some surprising consequences. Secondly, the claim put forth by Sornette et al. that large financial crashes may be heralded by accelerating precursory oscillations is also tested. It is shown that there is weak evidence for the existence of log-periodic precursors but the signal is probably too indistinct to allow for reliable predictions.

The understanding of the emergent behaviour of complex systems is probably one of the most intriguing challenges in modern theoretical physics. In the present Thesis we use novel data analysis techniques and numerical simulations in order to shed some light on the fundamental mechanisms involved in their dynamics. We divide the main core of the research into three parts, each of which address a specific, and formally well defined, issue. In the first part, we study the processes of self - organization and herding in the evolution of the stock market. The data analysis, carried out over the fluctuations of several international indices, shows an avalanche - like dynamics characterized by power laws and indicative of a critical state. Further evidence of criticality relates to the behaviour of the price index itself. In this case we observe a power law decline with superimposed embedded log - periodic oscillations which are possibly due to an intrinsic discrete scale invariance. A stochastic cellular automata, instead, is used to mimic an open stock market and reproduce the herding behaviour responsible for the large fluctuations observed in the price. The results underline the importance of the largest clusters of traders which, alone, can induce a large displacement between demand and supply and lead to a crash. The second part of the Thesis focuses on the role played by the complex network of interactions that is created among the elementary parts of the system itself. We consider, in particular, the influence of the so - called " scale - free " networks, where the distribution of connectivity follows a power law, on the antiferromagnetic Ising model and on a model of stochastic opinion formation. Novel features, not encountered on regular lattices, have been pointed out. In the former case a spin glass transition at low temperatures is present while, in the latter, the turbulent - like behaviour emerging from the model is found to be particularly robust against the indecision of the agents. The last part is left for a numerical investigation of an extremal dynamical model for evolution / extinction of species. We demonstrate how the mutual cooperation between them comes to play a fundamental role in the survival probability : a healthy environment can support even less fitted species. / Thesis (Ph.D.)--School of Chemistry and Physics, 2006.

Over the last few years there has been a surge of activity within the physics community in the emerging field of Econophysics—the study of economic systems from a physicist's perspective. Physicists tend to take a different view than economists and other social scientists, being interested in such topics as phase transitions and fluctuations. In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Fluctuations are driven by a stochastic component in the agents' forecasts. As the scale of the fluctuations is varied a critical phase transition is discovered. Unfortunately, this model is unable to generate realistic market dynamics. The second model discards the requirement of centralized trading. In this case the stochastic driving force is Gaussian-distributed "news events" which are public knowledge. Under variation of the control parameter the model exhibits two phase transitions: both a first- and a second-order (critical). The decentralized model is able to capture many of the interesting properties observed in empirical markets such as fat tails in the distribution of returns, a brief memory in the return series, and long-range correlations in volatility. Significantly, these properties only emerge when the parameters are tuned such that the model spans the critical point. This suggests that real markets may operate at or near a critical point, but is unable to explain why this should be. This remains an interesting open question worth further investigation. One of the main points of the thesis is that these empirical phenomena are not present in the stochastic driving force, but emerge endogenously from interactions between agents. Further, they emerge despite the simplicity of the modeled agents; suggesting complex market dynamics do not arise from the complexity of individual investors but simply from interactions between (even simple) investors. Although the emphasis of this thesis is on the extent to which multi-agent models can produce complex dynamics, some attempt is also made to relate this work with empirical data. Firstly, the trading strategy applied by the agents in the second model is demonstrated to be adequate, if not optimal, and to have some surprising consequences. Secondly, the claim put forth by Sornette et al. that large financial crashes may be heralded by accelerating precursory oscillations is also tested. It is shown that there is weak evidence for the existence of log-periodic precursors but the signal is probably too indistinct to allow for reliable predictions. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Kam Ying Chuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 81-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Overview of Hong Kong Stock Market --- p.3 / Chapter 2.1 --- Stock Exchange of Hong Kong --- p.3 / Chapter 2.2 --- Hang Seng Index --- p.4 / Chapter 2.3 --- Influences of the United States --- p.5 / Chapter 2.4 --- Hong Kong Government's Intervention --- p.6 / Chapter 3 --- Literature Review --- p.8 / Chapter 3.1 --- Stable and Student t Distributions --- p.8 / Chapter 3.2 --- Generalized Distribution --- p.10 / Chapter 3.3 --- Socio-economic Model --- p.11 / Chapter 3.4 --- Extreme Value Analysis --- p.11 / Chapter 4 --- Methodology --- p.14 / Chapter 4.1 --- Homogeneous Model --- p.15 / Chapter 4.2 --- Inhomogeneous Model --- p.15 / Chapter 4.3 --- Model Validity --- p.16 / Chapter 4.3.1 --- Exceedance Rate --- p.17 / Chapter 4.3.2 --- Distribution of Excesses --- p.17 / Chapter 4.3.3 --- Independence --- p.18 / Chapter 5 --- Data --- p.19 / Chapter 5.1 --- Minute-by-minute Returns --- p.20 / Chapter 5.2 --- Daily returns --- p.21 / Chapter 5.3 --- Explanatory Variables for the Inhomogeneous Model --- p.21 / Chapter 6 --- Empirical Results: Minute-by-minute Returns --- p.24 / Chapter 6.1 --- Shape Parameter k --- p.24 / Chapter 6.2 --- Location Parameter μ --- p.25 / Chapter 6.3 --- Scale Parameter σ --- p.26 / Chapter 6.4 --- Conditional Scale Parameter ψ --- p.27 / Chapter 6.5 --- Specification Test --- p.29 / Chapter 7 --- Empirical Results: Daily Returns --- p.29 / Chapter 7.1 --- Homogeneous Model --- p.30 / Chapter 7.2 --- Inhomogeneous Model --- p.31 / Chapter 7.2.1 --- Constant Term --- p.32 / Chapter 7.2.2 --- Dow Jones Industrial Average Returns --- p.33 / Chapter 7.2.3 --- Volatility Indicators --- p.34 / Chapter 7.2.4 --- Monday Dummy --- p.35 / Chapter 7.2.5 --- Time Trend --- p.36 / Chapter 7.2.6 --- Duration Dummy --- p.37 / Chapter 7.2.7 --- Indicator for the Behavior of the Previous Trading Day --- p.38 / Chapter 8 --- Conclusion --- p.39