This highly praised introductory treatment describes the parallels between statistical physics and finance - both those established in the 100-year long interaction between these disciplines, as well as new research results on financial markets. The random-walk technique, well known in physics, is also the basic model in finance, upon which are built, for example, the Black-Scholes theory of option pricing and hedging, plus methods of portfolio optimization. Here the underlying assumptions are assessed critically. Using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion, the book develops a more accurate description of financial markets based on random walks. With this approach, novel methods for derivative pricing and risk management can be formulated. Computer simulations of interacting-agent models provide insight into the mechanisms underlying unconventional price dynamics. It is shown that stock exchange crashes can be modelled in ways analogous to phase transitions and earthquakes, and sometimes have even been predicted successfully. This third edition of The Statistical Mechanics of Financial Markets especially stands apart from other treatments because it offers new chapters containing a practitioner's treatment of two important current topics in banking: the basic notions and tools of risk management and capital requirements for financial institutions, including an overview of the new Basel II capital framework which may well set the risk management standards in scores of countries for years to come.

This textbook describes parallels between statistical physics and finance - both those established in the 100-year-long interaction between these disciplines, as well as new research results on capital markets. The random walk, well known in physics, is also the basic model in finance, upon which are built, for example, the Black--Scholes theory of option pricing and hedging, or methods of risk control using diversification. Here the underlying assumptions are discussed using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion. On this basis, new theories of derivative pricing and risk control can be formulated. Computer simulations of interacting agent models of financial markets provide insights into the origins of asset price fluctuations. Stock exchange crashes can be modelled in ways analogous to phase transitions and earthquakes. These models allow for predictions. This study edition has been updated with a presentation of several new and significant developments, e.g. the dynamics of volatility smiles and implied volatility surfaces, path integral approaches to option pricing, a new and accurate simulation scheme for options, multifractals, the application of nonextensive statistical mechanics to financial markets, and the minority game. Moreover, the book was scanned for and corrected from errors, both typographical and in presentation.

This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative, coordinate-independent definition of path integrals, which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely products of distributions. The powerful FeynmanKleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent results. The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strong-coupling regime where they describe critical phenomena. Tunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and thelarge-order behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the large-order perturbation theory now also applies to small orders. Special attention is devoted to path integrals with topological restrictions needed to understand the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The ChernSimons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect. The relevance of path integrals to financial markets is discussed, and improvements of the famous BlackScholes formula for option prices are developed which account for the fact, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.

This book provides a unique insight into the latest breakthroughs in a consistent manner, at a level accessible to undergraduates, yet with enough attention to the theory and computation to satisfy the professional researcher Statistical physics addresses the study and understanding of systems with many degrees of freedom. As such it has a rich and varied history, with applications to thermodynamics, magnetic phase transitions, and order/disorder transformations, to name just a few. However, the tools of statistical physics can be profitably used to investigate any system with a large number of components. Thus, recent years have seen these methods applied in many unexpected directions, three of which are the main focus of this volume. These applications have been remarkably successful and have enriched the financial, biological, and engineering literature. Although reported in the physics literature, the results tend to be scattered and the underlying unity of the field overlooked.

This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics. Conceived nearly 150 years ago by Maxwell, Boltzmann and Gibbs, the BG theory, one of the greatest monuments of contemporary physics, exhibits many impressive successes in physics, chemistry, mathematics, and computational sciences. Presently, several thousands of publications by scientists around the world have been dedicated to its nonextensive generalization. A variety of applications have emerged in complex systems and its mathematical grounding is by now well advanced. Since the first edition release thirteen years ago, there has been a vast amount of new results in the field, all of which have been incorporated in this comprehensive second edition. Heavily revised and updated with new sections and figures, the second edition remains the go-to text on the subject. A pedagogical introduction to the BG theory concepts and their generalizations – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT’s, complex networks, among others – is presented in this book, as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions. Introduction to Nonextensive Statistical Mechanics is suitable for students and researchers with an interest in complex systems and statistical physics.

Tools and methods from complex systems science can have a considerable impact on the way in which the quantitative assessment of economic and financial issues is approached, as discussed in this thesis. First it is shown that the self-organization of financial markets is a crucial factor in the understanding of their dynamics. In fact, using an agent-based approach, it is argued that financial markets’ stylized facts appear only in the self-organized state. Secondly, the thesis points out the potential of so-called big data science for financial market modeling, investigating how web-driven data can yield a picture of market activities: it has been found that web query volumes anticipate trade volumes. As a third achievement, the metrics developed here for country competitiveness and product complexity is groundbreaking in comparison to mainstream theories of economic growth and technological development. A key element in assessing the intangible variables determining the success of countries in the present globalized economy is represented by the diversification of the productive basket of countries. The comparison between the level of complexity of a country's productive system and economic indicators such as the GDP per capita discloses its hidden growth potential.

This volume is a collection of original papers and reviews in honour of James McGuire, one of the pioneers of integrable models in statistical physics. The broad range of articles offers a timely perspective on the current status of statistical mechanics, identifying both recent results as well as future challenges. The work contains a number of overviews of standard topics such as exactly solved lattice models and their various applications in statistical physics, from models of strongly correlated electrons to the conformational properties of polymer chains. It is equally wide ranging in its coverage of new directions and developing fields including quantum computers, financial markets, chaotic systems, Feigenbaum scaling, proteins, brain behaviour, immunology, Markov superposition, Bose-Einstein condensation, random matrices, exclusion statistics, vertex operator algebras and D-unsolvability.The level of coverage is appropriate for graduate students. It will be equally of interest to professional physicists who want to learn about progress in statistical physics in recent years. Experts will find this work useful because of its broad sweep of topics and its discussion of remaining unsolved problems.

This book explains how standard micro-founded macroeconomics is misguided and proposes an alternative method based on statistical physics. The Great Recession following the bankruptcy of Lehman Brothers in September 2015 amply demonstrated that mainstream micro-founded macroeconomics was in trouble. The new approach advanced in this book reasonably explains important macro-problems such as employment, business cycles, growth, and inflation/deflation. The key concept is demand failures, which modern micro-founded macroeconomics has ignored. “It (Chapter 3) captures analytically a good part of the intuition that underlies the Keynesian economics of people like Tobin and me.” Robert Solow, Emeritus Institute Professor of Economics, Massachusetts Institute of Technology, Nobel Laureate in Economics, 1987 “Professor Hiroshi Yoshikawa provides a unique synthesis of statistical physics and macro-economic theory in order to confront the dismal failure in economics and in finance to understand how an economy or a financial market works, given the heterogeneous decision making of many different individual interacting actors. Economics has failed in this regard with the naive and often misleading concept of “representative agents.” The author presents many insights on the historical development, concepts, and errors made by the most illustrious economists in the past. This book should be essential readings for any economics students as well as academic researchers and policy makers, who should learn to bring back good-sense thinking in their impactful decisions.” Didier Sornette, Professor on the Chair of Entrepreneurial Risks at the Swiss Federal Institute of Technology Zurich (ETH Zurich)

This book systematically provides a prospective integrated approach for complexity social science in its view of statistical physics and mathematics, with an impressive collection of the knowledge and expertise of leading researchers from all over the world. The book mainly covers both finitary methods of statistical equilibrium and data-driven analysis by econophysics. The late Professor Masanao Aoki of UCLA, who passed away at the end of July 2018, in his later years dedicated himself to the reconstruction of macroeconomics mainly in terms of statistical physics. Professor Aoki, who was already an IEEE fellow, was also named an Econometric Society Fellow in 1979. Until the early 1990s, however, his contributions were focused on the new developments of a novel algorithm for the time series model and their applications to economic data. Those contributions were undoubtedly equivalent to the Nobel Prize-winning work of Granger's "co-integration method". After the publications of his New Approaches to Macroeconomic Modeling and Modeling Aggregate Behavior and Fluctuations in Economics, both published by Cambridge University Press, in 1996 and 2002, respectively, his contributions rapidly became known and spread throughout the field. In short, these new works challenged econophysicists to develop evolutionary stochastic dynamics, multiple equilibria, and externalities as field effects and revolutionized the stochastic views of interacting agents. In particular, the publication of Reconstructing Macroeconomics, also by Cambridge University Press (2007), in cooperation with Hiroshi Yoshikawa, further sharpened the process of embodying “a perspective from statistical physics and combinatorial stochastic processes” in economic modeling. Interestingly, almost concurrently with Prof. Aoki’s newest development, similar approaches were appearing. Thus, those who were working in the same context around the world at that time came together, exchanging their results during the past decade. In memory of Prof. Aoki, this book has been planned by authors who followed him to present the most advanced outcomes of his heritage.