Chaos & Fractals in Financial Markets PDF
179 Pages·2001·1.11 MB·English
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Chaos and Fractals inFinancial Markets, Part 1The rolling of the golden apple. I meet chaos. Preliminarypictures and poems. Dynamical systems. What is chaos? I'msensitive, don't perturb me. Why chaos? How fast doforecasts go wrong? — the Lyapunov exponent. Simplecalculation using a Lyapunov exponent. Enough for now.Problems.Chaos and Fractals inFinancial Markets, Part 2The French gambler and the pollen grains. The square rootof time. Normal versus lognormal. How big is it? History'sfirst fractal. Fractal time. Probability is a one-pound jar ofjelly. Problems and answers.Chaos and Fractals inFinancial Markets, Part 3Hazardous world. Coin flips and Brownian motion. A simplestochastic fractal. Sierpinski and Cantor revisited. Blobmeasures are no good. Coastlines and Koch curves. Using aHausdorff measure. Jam session.Chaos and Fractals inFinancial Markets, Part 4Gamblers, zero-sets, and fractal mountains. Futures tradingand the gambler's ruin problem. An example. Gauss versusCauchy. Location and scale.Chaos and Fractals inFinancial Markets, Part 5Louis Bachelier visits the New York Stock Exchange.Bachelier's scale for stock prices. Volatility. Fractal sums ofrandom variables. Some fun with logistic art. Julia sets.Chaos and Fractals inFinancial Markets, Part 6Prechter's drum roll. Symmetric stable distributions and thegold mean law. The Fibonacci dynamical system.Chaos and Fractals inFinancial Markets, Part 7Grow brain. Hurst, hydrology and the annual flooding of theNile. Calculating the Hurst exponent. A misunderstanding toavoid. Bull and bear markets.These articles are parts of a work in progress. ©1999-2001 J. Orlin Grabbe. A
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