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An Introduction to Econophysics

R. N. Mantegna and H. E. Stanley

posted on 01 April 1999

reviewed by Dietrich Stauffer

Finally, Gene Stanley who seems to have invented the word econophysics, finished
his book about it, with Rosario Mantegna who organized in Palermo the last
European econophysics meeting. The authors deal with the description and
analysis of real market fluctuations. Their own work on company growth and
similar aspects is not described here; also microscopic market models are only
cited, not discussed.

Roughly half of the books deals with the mathematical methods. After an
introduction the second chapter explains the efficient market hypothesis: The
expectation value E(Y) of tomorrow's price Y is just today's price. Chapter 3
deal with random walks, the central limit theorem, and the Berry-Esseen theorem.

Levy-stable distributions and similar processes are dealt with in chapter 4.
Then the question of proper time scales is explained, followed by a definition
of autocorrelation functions of time.

Chapter 7 on stochastic models of price dynamics shows why Gaussian
distributions are in general not realistic, while truncated Levy flights are.
Scaling and the deviations from scaling are explained in chapter 8 for the
Standard and Poor 500 index, The ARCH and GARCH descriptions loved by many
economists are described in ch. 9, the analogy with turbulence loved by some
physicists in ch. 10. Correlations and anticorrelations between stocks, chapter
11, lead to a classification of companies into groups; ultrametricity describes
these classifications according to ch. 12. The last two chapters introduce in
a simple way the various "derivatives" by which risks can be shifted, and the
related Black-Scholes formula and its limitations.

Each of these chapters ends with a summary, and an appendix lists the notation
for each chapter as well as a definition of martingales.

I think this book is a useful complement to the one of Bouchaud and Potters;
had I written it I would have tried to avoid some mathematics. This review
is based on a preprint of 152 pages kindly sent to me by the authors.



I want buy this book. How to get it?

Sutanto Sastraredja

just google "An Introduction to Econophysics", then you'll get a link to some online book store.