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IN 1959-61, while the huge Saarinen-designed research laboratory at Yorktown Heights was being built, much of IBM's Research was housed nearby. My group occupied one of the many little houses on the Lamb Estate complex which had been a sanatorium housing wealthy alcoholics. The picture below was taken about 1960. It shows from right to left, T. e. Hu, now at the University of California, Santa Barbara. I am next, staring at a network I have just written on the blackboard. Then comes Paul Gilmore, late of the University of British Columbia, then (seated) Richard Levitan, now retired, and at the left is Benoit Mandelbrot. x FOREWORD EF Even in a Lamb Estate populated exclusively with bright research­ oriented people, Benoit always stood out. His thinking was always fresh, and I enjoyed talking with him about any subject, whether technical, poli­ tical, or historical. He introduced me to the idea that distributions having infinite second moments could be more than a mathematical curiosity and a source of counter-examples. This was a foretaste of the line of thought that eventually led to fractals and to the notion that major pieces of the physical world could be, and in fact could only be, modeled by distrib­ utions and sets that had fractional dimensions. Usually these distributions and sets were known to mathematicians, as they were known to me, as curiosities and counter-intuitive examples used to show graduate students the need for rigor in their proofs.

Finance --- Fractals --- Scaling (Social sciences) --- 303.0 --- 305.6 --- 305.91 --- AA / International- internationaal --- 336.7 --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- 336.7 Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- Scale analysis (Social sciences) --- Scales of measurement --- Social sciences --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Statistical methods --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken) --- Risicotheorie, speltheorie. Risicokapitaal. Beslissingsmodellen --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Methodology --- Finances --- Statistical science --- Differential geometry. Global analysis --- Analytical topology --- Stochastic processes --- Mathematical statistics --- Financial analysis --- Fractals. --- Scaling (Social sciences). --- Statistical methods. --- Finance - Statistical methods

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Stochastic processes --- Geometry --- Mathematical models --- Fractals --- Géométrie --- Modèles mathématiques --- Processus stochastiques --- Fractales --- 517.987 --- Random processes --- Probabilities --- Models, Mathematical --- Simulation methods --- Mathematics --- Euclid's Elements --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Fractals. --- Geometry. --- Mathematical models. --- Stochastic processes. --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Géométrie --- Modèles mathématiques

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Marché financier --- Analyse financière --- Actions (Titre de société) --- Valeurs mobilières --- Gestion du risque --- Prix --- Actions (Titres de société) --- AA / International- internationaal --- 339.40 --- Vermogenbeheer. financiële analyse (algemeenheden). --- Marché financier --- Analyse financière --- Actions (Titre de société) --- Valeurs mobilières --- Capital market --- Investment analysis --- Stocks --- Securities --- Risk management --- Prices --- Vermogenbeheer. financiële analyse (algemeenheden) --- Stocks - Prices --- Acqui 2006

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Kunst en natuur mathematische modellen fractalen --- Kunst en geometrie --- 7.013 --- Kunst verhouding, vorm, ritme --- Fractales --- Modèle mathématique --- 517.987 --- 514.17 --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Convex sets. Geometric figure arrangements. Geometric inequalities --- Fractals. --- Mathematics (General) --- 514.17 Convex sets. Geometric figure arrangements. Geometric inequalities --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Mathematics (General). --- Fractals --- Geometry --- Mathematical models --- Stochastic processes --- #ABIB:altk --- #TELE:SISTA --- Random processes --- Probabilities --- Models, Mathematical --- Simulation methods --- Mathematics --- Euclid's Elements --- Kunst en natuur ; mathematische modellen ; fractalen --- Kunst ; verhouding, vorm, ritme --- #WSCH:AAS2 --- #WSCH:MODS --- Geometry. --- Mathematical models. --- Stochastic processes. --- Basic Sciences. Mathematics --- Statistical methods --- Probability. --- Mathematics. --- Géométrie --- Modèles mathématiques --- Processus stochastiques --- Geometric measure theory --- Mesure géométrique, Théorie de la --- Fractales. --- Geometric probabilities. --- Probabilités géométriques. --- Géométrie analytique --- Mathématiques --- Fractal geometry of nature --- Probabilite --- Turbulence --- Fractale geometry --- Geometrie --- Geometrie fractale --- Theorie geometrique de la mesure

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Chaotic behavior in systems. --- Chaos (théorie des systèmes) --- Mathématiques financières --- Business mathematics --- Fractales --- Mouvement brownien