Book Description
Portfolio analysis and optimization, together with the associated risk assessment and management, require knowledge of the likely distributions of returns at different time scales and insights into the nature and properties of dependences between the different assets.
This book offers an original and thorough treatment of these two domains, focusing mainly on the concepts and tools that remain valid for large and extreme price moves. Strong emphasis is placed on the theory of copulas and their empirical testing and calibration, because they offer intrinsic and complete measures of dependences.
Extreme Financial Risks will be useful to:
students looking for a general and in-depth introduction to the field;
financial engineers, economists, econometricians, actuarial professionals;
researchers and mathematicians looking for a synoptic view comparing the pros and cons of different modelling strategies; and
quantitative practitioners for the insights offered on the subtleties and the many dimensional components of both risk and dependence.
In toto, the content of this book will also be useful to a broader scientific community interested in quantifying the complexity of many natural and artificial processes in which a growing emphasis is on the role and importance of extreme phenomena.
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Interacting Particle Systems (Classics in Mathematics)
Thomas M. Liggett
Manufacturer: Springer
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ASIN: 3540226176 |
Book Description
From the reviews
"[...] This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. …The high quality of this work, [...] , makes a fascinating subject and its open problem as accessible as possible. [...]"
F.L. Spitzer
in Mathematical Reviews, 1986
"[...] However, it can be said that the author has succeeded in what even experts are seldom able to achieve: To write a clearcut and inspiring book on his favorite subject which meets most, if not all requirements which can be imposed on a comprehensive text on an important new field. The author can be congratulated on his excellent presentation of the theory of interacting particle systems. The book is highly recommended to everyone who works on or is interested in this subject: to probabilists, physicists and theoretical biologists. [...]"
G. Rosenkranz in
Methods of Information in Medicine, 1986
Product Description
Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods. That variety stimulates new ideas and developments from many different places, and there is much to be gained from cross-fertilization. This book presents five expository essays by leaders in the field, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts. The essays derive from tutorial lectures at an interdisciplinary program at the Institute for Mathematical Sciences, Singapore, which exploited the exciting ways in which MCMC spreads across different disciplines.
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Regular and Chaotic Dynamics (Applied Mathematical Sciences)
A.J. Lichtenberg , and
M.A. Lieberman
Manufacturer: Springer
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Binding: Hardcover
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ASIN: 0387977457 |
Book Description
This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.
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Mathematical Theory of Nonequilibrium Steady States
Da-Quan Jiang ,
Min Qian , and
Ming-Ping Qian
Manufacturer: Springer
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ASIN: 3540206116 |
Book Description
This volume provides a systematic mathematical exposition of the conceptual problems of nonequilibrium statistical physics, such as entropy production, irreversibility, and ordered phenomena. Markov chains, diffusion processes, and hyperbolic dynamical systems are used as mathematical models of physical systems. A measure-theoretic definition of entropy production rate and its formulae in various cases are given. It vanishes if and only if the stationary system is reversible and in equilibrium. Moreover, in the cases of Markov chains and diffusion processes on manifolds, it can be expressed in terms of circulations on directed cycles. Regarding entropy production fluctuations, the Gallavotti-Cohen fluctuation theorem is rigorously proved.
Customer Reviews:
Impressive work from a highly productive group in China.......2006-06-26
I really enjoy reading many chapters from this book.
This book is unusual in a sense that it is written by
two probabilists and one applied mathematician on important physics and dynamical problems. There is very good coverage on
Markov chain theory, especially reversibility and information theory. The statistical physics theory is also very well presented, as well as statistical theory on dynamical systems. The authors are teachers at China's prestigous Peking University Math Sci School. The first author is a student of the senior second and third author, who are a brother-sister team, highly accomplished and very seasoned researchers in the subject area. I think this monograph will benefit researchers as well as students who first get into this very active research area.
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Global Analysis in Mathematical Physics: Geometric and Stochastic Models (Applied Mathematical Sciences)
Yuri Gliklikh
Manufacturer: Springer
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ASIN: 0387948678 |
Book Description
This book gives a common treatment to three areas of application of Global analysis to Mathematical Physics previously considered quite distant from each other. These areas are the geometry of manifolds applied to classical mechanics, stochastic differential geometry used in quantum and statistical mechanics, and infinite-dimensional differential geometry fundamental for hydrodynamics.
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An Introduction to Quantum Stochastic Calculus (Monographs in Mathematics)
K.R. Parthasarathy
Manufacturer: Birkhäuser Basel
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ASIN: 3764326972 |
Book Description
"Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly
"This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews
An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features:
The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle.
Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields.
Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions.
The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.
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Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach (Probability and its Applications)
Nils Berglund , and
Barbara Gentz
Manufacturer: Springer
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Binding: Hardcover
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ASIN: 1846280389 |
Book Description
Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation theory, allows the domains of concentration for typical sample paths to be determined, and provides precise estimates on the transition probabilities between these domains.
In addition to the detailed presentation of the set-up and mathematical results, applications to problems in physics, biology, and climatology are discussed. The emphasis lies on noise-induced phenomena such as stochastic resonance, hysteresis, excitability, and the reduction of bifurcation delay.
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Dynamics of Stochastic Systems
Valery I. Klyatskin
Manufacturer: Elsevier Science
ProductGroup: Book
Binding: Paperback
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ASIN: 0444517960
Release Date: 2005-12-15 |
Book Description
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''oil slicks''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.
Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.
The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data.
This raises a host of challenging mathematical issues. One could rarely solve such systems exactly (or approximately) in a closed analytic form, and their solutions depend in a complicated implicit manner on the initial-boundary data, forcing and system's (media) parameters . In mathematical terms such solution becomes a complicated "nonlinear functional" of random fields and processes.
Part I gives mathematical formulation for the basic physical models of transport, diffusion, propagation and develops some analytic tools.
Part II sets up and applies the techniques of variational calculus and stochastic analysis, like Fokker-Plank equation to those models, to produce exact or approximate solutions, or in worst case numeric procedures. The exposition is motivated and demonstrated with numerous examples.
Part III takes up issues for the coherent phenomena in stochastic dynamical systems, described by ordinary and partial differential equations, like wave propagation in randomly layered media (localization), turbulent advection of passive tracers (clustering).
Each chapter is appended with problems the reader to solve by himself (herself), which will be a good training for independent investigations.
· This book is translation from Russian and is completed with new principal results of recent research.
· The book develops mathematical tools of stochastic analysis, and applies them to a wide range of physical models of particles, fluids, and waves.
· Accessible to a broad audience with general background in mathematical physics, but no special expertise in stochastic analysis, wave propagation or turbulence
Book Description
Nonstationarity is another name for intermittency, a phenomenon which affects many physical processes. Data collected in many R&D programs frequently exhibit nonstationary features, and problems inherent in the analysis of such data are profound. The premier objective of these proceedings is to consolidate recent developments in nonstationary analysis. A second objective is to delineate open problems. A by-product will hopefully be a bridging of the gap between related governmental needs, and the present-day research capabilities of both academics and non-academics alike.
Books:
- Feedback Control of Dynamic Systems (5th Edition)
- Finite Mathematics for Business, Economics, Life Sciences and Social Sciences (11th Edition)
- Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics)
- Focal Liver Lesions: Detection, Characterization, Ablation (Medical Radiology / Diagnostic Imaging)
- Foundations of Algorithms Using C++ Pseudocode, Third Edition
- Functional Analysis
- Fundamental Methods of Mathematical Economics
- Fundamentals of Atmospheric Modeling
- Fundamentals of Power Electronics (Second Edition)
- Galois Theory (Universitext)
Books Index
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