the statistical mechanics of financial markets

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The Statistical Mechanics Of Financial Markets

Author : Johannes Voit
ISBN : 9783662051252
Genre : Mathematics
File Size : 48. 70 MB
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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.

Outlines And Highlights For The Statistical Mechanics Of Financial Markets By Johannes Voit

Author : Cram101 Textbook Reviews
ISBN : 161830285X
Genre : Education
File Size : 34. 56 MB
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Never HIGHLIGHT a Book Again! Virtually all of the testable terms, concepts, persons, places, and events from the textbook are included. Cram101 Just the FACTS101 studyguides give all of the outlines, highlights, notes, and quizzes for your textbook with optional online comprehensive practice tests. Only Cram101 is Textbook Specific. Accompanys: 9783642065781 .

Scaling Limits In Statistical Mechanics And Microstructures In Continuum Mechanics

Author : Errico Presutti
ISBN : 9783540733058
Genre : Mathematics
File Size : 67. 89 MB
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Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.

Introduction To Nonextensive Statistical Mechanics

Author : Constantino Tsallis
ISBN : 9780387853581
Genre : Science
File Size : 85. 70 MB
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Metaphors, generalizations and unifications are natural and desirable ingredients of the evolution of scientific theories and concepts. Physics, in particular, obviously walks along these paths since its very beginning. This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics, one of the greatest monuments of contemporary physics. Conceived more than 130 years ago by Maxwell, Boltzmann and Gibbs, the BG theory exhibits uncountable – some of them impressive – successes in physics, chemistry, mathematics, and computational sciences, to name a few. Presently, more than two thousand publications, by over 1800 scientists around the world, have been dedicated to the nonextensive generalization. Remarkable applications have emerged, and its mathematical grounding is by now relatively well established. A pedagogical introduction to its concepts – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT’s, 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. This is the first pedagogical book on the subject, written by the proponent of the theory Presents many applications to interdisciplinary complex phenomena in virtually all sciences, ranging from physics to medicine, from economics to biology, through signal and image processing and others Offers a detailed derivation of results, illustrations and for the first time detailed presentation of Nonextensive Statistical Mechanics

Econophysics

Author : Gheorghe Săvoiu
ISBN : 9780124046269
Genre : Business & Economics
File Size : 20. 87 MB
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The remarkable evolution of econophysics research has brought the deep synthesis of ideas derived from economics and physics to subjects as diverse as education, banking, finance, and the administration of large institutions. The original papers in this collection present a broad summary of these advances, written by interdisciplinary specialists. Included are studies on subjects in the development of econophysics; on the perspectives offered by econophysics on large problems in economics and finance, including the 2008-9 financial crisis; and on higher education and group decision making. The introductions and insights they provide will benefit everyone interested in applications of this new transdisciplinary science. Ten papers present an updated version of the origins, issues, and applications of econophysics Economics and finance chapters consider lessons learned from the 2008-9 financial crisis Sociophysics chapters propose new thinking on educational reforms and group decision making

Theory Of Financial Risk And Derivative Pricing

Author : Jean-Philippe Bouchaud
ISBN : 9781139440271
Genre : Business & Economics
File Size : 80. 10 MB
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Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets

Author : Hagen Kleinert
ISBN : 9789814273572
Genre : Mathematics
File Size : 76. 98 MB
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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 Feynman-Kleinert 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 the large-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 ChernoOe1/4OC Simons 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 BlackoOe1/4OC Scholes 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."

Statistical Mechanics For Athermal Fluctuation

Author : Kiyoshi Kanazawa
ISBN : 9789811063329
Genre : Science
File Size : 71. 87 MB
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The author investigates athermal fluctuation from the viewpoints of statistical mechanics in this thesis. Stochastic methods are theoretically very powerful in describing fluctuation of thermodynamic quantities in small systems on the level of a single trajectory and have been recently developed on the basis of stochastic thermodynamics. This thesis proposes, for the first time, a systematic framework to describe athermal fluctuation, developing stochastic thermodynamics for non-Gaussian processes, while thermal fluctuations are mainly addressed from the viewpoint of Gaussian stochastic processes in most of the conventional studies. First, the book provides an elementary introduction to the stochastic processes and stochastic thermodynamics. The author derives a Langevin-like equation with non-Gaussian noise as a minimal stochastic model for athermal systems, and its analytical solution by developing systematic expansions is shown as the main result. Furthermore, the a uthor shows a thermodynamic framework for such non-Gaussian fluctuations, and studies some thermodynamics phenomena, i.e. heat conduction and energy pumping, which shows distinct characteristics from conventional thermodynamics. The theory introduced in the book would be a systematic foundation to describe dynamics of athermal fluctuation quantitatively and to analyze their thermodynamic properties on the basis of stochastic methods.

Studies Of Credit And Equity Markets With Concepts Of Theoretical Physics

Author : Michael Münnix
ISBN : 9783834883285
Genre : Mathematics
File Size : 89. 38 MB
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Michael C. Münnix analyses the statistical dependencies in financial markets and develops mathematical models using concepts and methods from physics. The author focuses on aspects that played a key role in the emergence of the recent financial crisis: estimation of credit risk, dynamics of statistical dependencies, and correlations on small time-scales. He visualizes the findings for various large-scale empirical studies of market data. The results give novel insights into the mechanisms of financial markets and allow conclusions on how to reduce financial risk significantly.

Advances In Computer Science And Engineering

Author : Dehuai Zeng
ISBN : 9783642279485
Genre : Computers
File Size : 82. 50 MB
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This book includes the proceedings of the second International Conference on Advances in Computer Science and Engineering (CES 2012), which was held during January 13-14, 2012 in Sanya, China. The papers in these proceedings of CES 2012 focus on the researchers’ advanced works in their fields of Computer Science and Engineering mainly organized in four topics, (1) Software Engineering, (2) Intelligent Computing, (3) Computer Networks, and (4) Artificial Intelligence Software.

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