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The real world is perceived and broken down as data, models and
algorithms in the eyes of physicists and engineers. Data is noisy
by nature and classical statistical tools have so far been
successful in dealing with relatively smaller levels of randomness.
The recent emergence of Big Data and the required computing power
to analyse them have rendered classical tools outdated and
insufficient. Tools such as random matrix theory and the study of
large sample covariance matrices can efficiently process these big
data sets and help make sense of modern, deep learning algorithms.
Presenting an introductory calculus course for random matrices, the
book focusses on modern concepts in matrix theory, generalising the
standard concept of probabilistic independence to non-commuting
random variables. Concretely worked out examples and applications
to financial engineering and portfolio construction make this
unique book an essential tool for physicists, engineers, data
analysts, and economists.
There has been recently some interdisciplinary convergence on a
number of precise topics which can be considered as prototypes of
complex systems. This convergence is best appreciated at the level
of the techniques needed to deal with these systems, which include:
1) A domain of research around a multiple point where statistical
physics, information theory, algorithmic computer science, and more
theoretical (probabilistic) computer science meet: this covers some
aspects of error correcting codes, stochastic optimization
algorithms, typical case complexity and phase transitions,
constraint satisfaction problems.
2) The study of collective behavior of interacting agents, its
impact on understanding some types of economical and financial
problems, their link to population and epidemics dynamics, game
theory, social, biological and computer networks and evolution.
The present book is the written version of the lectures given
during the Les Houches summer school session on "Complex Systems,"
devoted to these emerging interdisciplinary fields. The lectures
consist both in a number of long methodological courses
(probability theory, statistical physics of disordered systems,
information theory, network structure and evolution, agent-based
economics and numerical methods) and more specific, 'problem
oriented' courses. Lecturers are all leading experts in their
field; they have summarized recent results in a clear and
authoritative manner. The "Les Houches lecture notes" have a long
tradition of excellence and are often found to be useful for a
number of years after they were written.
The book is of interest to students and researchers with various
backgrounds: probability theory, computer science, information
theory, physics, finance, biology, etc.
.Topical and comprehensive survey of the emerging,
interdisciplinary field of "Complex Systems," covered by recognized
world experts
."Les Houches lectures notes": a long tradition of excellence and
long-lasting impact
.Of interest to a broad audience (mathematics, physics, biology,
informatics, finance, geology, etc.)
.Some applications may have concrete impact
.Selected topics in complex systems: forefront of research in the
field"
The widespread availability of high-quality, high-frequency data
has revolutionised the study of financial markets. By describing
not only asset prices, but also market participants' actions and
interactions, this wealth of information offers a new window into
the inner workings of the financial ecosystem. In this original
text, the authors discuss empirical facts of financial markets and
introduce a wide range of models, from the micro-scale mechanics of
individual order arrivals to the emergent, macro-scale issues of
market stability. Throughout this journey, data is king. All
discussions are firmly rooted in the empirical behaviour of real
stocks, and all models are calibrated and evaluated using recent
data from Nasdaq. By confronting theory with empirical facts, this
book for practitioners, researchers and advanced students provides
a fresh, new, and often surprising perspective on topics as diverse
as optimal trading, price impact, the fragile nature of liquidity,
and even the reasons why people trade at all.
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.
This is a book about laser cooling, a new research field with many potential applications. The authors present an original approach, using the tools and concepts of statistical physics. A new understanding of laser cooling, both intuitive and quantitative, is obtained. The volume also comprises a case study allowing non-Gaussian (Lévy) statistics, a technique being used more frequently in many different fields.
This is a book about laser cooling, a new research field with many potential applications. The authors present an original approach, using the tools and concepts of statistical physics. A new understanding of laser cooling, both intuitive and quantitative, is obtained. The volume also comprises a case study allowing non-Gaussian (Lévy) statistics, a technique being used more frequently in many different fields.
Summarizing market data developments, some inspired by statistical physics, this book explains how to better predict the actual behavior of financial markets with respect to asset allocation, derivative pricing and hedging, and risk control. Risk control and derivative pricing are major concerns to financial institutions. The need for adequate statistical tools to measure and anticipate amplitude of potential moves of financial markets is clearly expressed, in particular for derivative markets. Classical theories, however, are based on assumptions leading to systematic (sometimes dramatic) underestimation of risks. First edition Hb (2000): 0-521-78232-5
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