QuoteWhat is a fractal?
B. Mandelbrot
A rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole.
Mathematical
A set of points whose fractal dimension exceeds its topological dimension.
QuoteFOREWARD
This work follows and largely replaces my 1977 Essay, FRACTALS: FORM, CHANCE AND DIMENSION, which had followed and largely replaced my 1975 Essay in French, LES OBJETS FRACTALS: FORME, HASARD ET DIMENSION. Each stage involved new art, a few deletions, extensive rewriting that affected nearly every section, additions devoted to my older work, and - most important - extensive additions devoted to new developments.
Richard F. Voss made an essential contribution to the 1977 Essay and to this work, especially by designing and now redesigning the fractal flakes, most landscapes, and the planets. The programs for many striking illustrations new to this Essay are by V. Alan Norton.
Other invaluable, close, long-term associates were Sigmund W. Handelman, then Mark R. Laff, for computation and graphics, and H. Catharine Dietrich, then Janis T. Riznychok, for editing and typing.
Individual acknowledgments for the programs behind the illustrations and for other specific assistance are found after the list of references at the end of the volume.
For their backing of my research and my books, I am deeply indebted to the Thomas J. Watson Research Center of the International Business Machines Corporation. As Group Manager, Department Director, and now Director of Research, IBM Vice President Ralph E. Gomory imagined ways of sheltering and underwriting my work when it was a gamble, and now of giving it all the support I could use.
My first scientific publication came out on April 30, 1951. Over the years, it had seemed to many that each of my investigations was aimed in a different direction. But this apparent disorder was misleading: it hid a strong unity of purpose, which the present Essay, like its two predecessors, is intended to reveal. Against odds, most of my works turn out to have been the birth pangs of a new scientific discipline.
QuoteIssuers are pulling the plug on exchange-traded funds faster than ever, and yours could be the next to go offline. A Bloomberg Intelligence count found that 44 U.S.-listed ETFs closed during June, the second-highest monthly total on record.
QuoteA trio of current, powerful financial trends explains the extension of private market assets into individual investors' portfolios.
QuoteMarkets knew they weren't going to get an answer to what the Federal Reserve would do next — so-called forward guidance — when the central bank's chairman, Kevin Warsh, spoke on Friday morning. The biggest question looming over Warsh's highly anticipated speech was whether he would clarify how the Fed will respond to rising inflation.
QuoteWarsh has no credibility. However don't get too worked up over Warsh not providing much information because the bond vigilantes will firmly drive economic policy, not matter what the Fed does.
Don't freak out about Kevin Warsh's 'credibility'
https://finance.yahoo.com/economy/policy/articles/don-t-freak-kevin-warsh-173035312.html
Economists and analysts kind of lost their minds about what they heard from new Federal Reserve Chairman Kevin Warsh Wednesday. Or, more precisely, what they didn't hear.
QuotePreface
Physicists are currently contributing to the modeling of 'complex systems' by using tools and methodologies developed in statistical mechanics and theoretical physics. Financial markets are remarkably well-defined complex systems, which are continuously monitored - down to time scales of seconds. Further, virtually every economic transaction is recorded, and an increasing fraction of the total number of recorded economic data is becoming accessible to interested researchers. Facts such as these make financial markets extremely attractive for researchers interested in developing a deeper understanding of modeling of complex systems.
Economists - and mathematicians - are the researchers with the longer tradition in the investigation of financial systems. Physicists, on the other hand, have generally investigated economic systems and problems only occasionally. Recently, however, a growing number of physicists is becoming involved in the analysis of economic systems. Correspondingly, a significant number of papers of relevance to economics is now being published in physics journals. Moreover, new interdisciplinary journals - and dedicated sections of existing journals - have been launched, and international conferences are being organized.
In addition to fundamental issues, practical concerns may explain part of the recent interest of physicists in finance. For example, risk management, a key activity in financial institutions, is a complex task that benefits from a multidisciplinary approach. Often the approaches taken by physicists are complementary to those of more established disciplines, so including physicists in a multidisciplinary risk management team may give a cutting edge to the team, and enable it to succeed in the most efficient way in a competitive environment.
This book is designed to introduce the multidisciplinary field of econophysics, a neologism that denotes the activities of physicists who are working on economics problems to test a variety of new conceptual approaches deriving from the physical sciences. The book is short, and is not designed to review all the recent work done in this rapidly developing area. Rather, the book offers an introduction that is sufficient to allow the current literature to be profitably read. Since this literature spans disciplines ranging from financial mathematics and probability theory to physics and economics, unavoidable notation confusion is minimized by including a systematic notation list in the appendix.
