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Prelude: Introducing a Maverick in Science xvii Benoit Mandelbrot, the "father" of fractals, has made a career of going against the prevailing fashions in science. Part I. The Old Way Chapter 1 Risk, Ruin, and Reward 3 "Mlodern" financial theory is founded on a few, shaky myths that lead us to underestimate the real risk of financial markets. Chapter II By the Toss of a Coin or the Flight of an Arrow? 25 lHow the operations of mere chance can be used to study a financial market. Chapter HIf Bachelier and His Legacy 43 The study offinancial theory began a century ago with a brilliant but undervalued French mathematician, Louis Bachelier, Chapter IV The flouse of \lodern Finance 59 How the edifice of: modern Ifin nc ia theory-- valuing assets, building portfolios and assessing risk vu ws erected on Bachelier's worh. Chapter V T'he Case Against the Modern Theory of Finance 79 Orthodox jinancial theorn is riddled with false assumptions and wrong results. A sunnmmary of the evidence agatinst it Pictorial E:saiv: Images of the \ibnorotal 88 Part II. The New Way Chapter VI Turbulent \Irirkets: A Preview I1i Financial markets are tiirb lent like the windl or the flood ,n introduction to the fractal view c of finr nce. Chapter VII Studies in Roughness: A Fractal Primer 123 How is a stock-price c hart like the leaves of a fer?. A survey of fractal geometry Pictorial Essay: A Fractal (Gallery 132 Chapter VIII The Mystery of Cotton 147 Ihe first clue to the fractal view of finance came in a study of cotton by Mandelbrot. An uccount of his scientitic journey. Chlapter TX Long Memory, from the Nile to the Marketplace 1I7 -lihe second clue to fractal linance came from lifelong study of the Nile River by an Eiiglish hydrologist, H.E. Hurst. Chapter X Noah, Joseph, and Market Bubbles 197 The two critical features of financial markets are wild price swings and long-term dependence--the Noah Effect and the Joseph Effect. Chapter XI The Multifractal Nature of "Trading Time 207 In financial markets, time speeds up and slows down--as described in the multifractal model of marIkets. Part III. The Way Ahead Chapter XI Ten Heresies of Finance 225 How do financial morkers really work? A list of key insights provided by the fractal view of finance. Chapter XIII In the Lab 253 So how can the study of fractals change finance? A program for future research. Notes 277 Bibliography 303