Chaos and Fractals in Financial Markets

Speech Presented to Eris Society

The rolling of the golden apple. I meet chaos. Preliminary pictures and poems. Dynamical systems. What is chaos? I'm sensitive, don't perturb me. Why chaos? How fast do forecasts go wrong?--the Lyapunov exponent. Simple calculation using a Lyapunov exponent. Enough for now. Problems.

The French gambler and the pollen grains. The square root of time. Normal versus lognormal. How big is it? History's first fractal. Fractal time. Probability is a one-pound jar of jelly. Problems and answers.

Hazardous world. Coin flips and Brownian motion. A simple stochastic fractal. Sierpinski and Cantor revisited. Blob measures are no good. Coastlines and Koch curves. Using a Hausdorff measure. Jam session.

Gamblers, zero-sets, and fractal mountains. Futures trading and the gambler's ruin problem. An example. Gauss versus Cauchy. Location and scale.

Louis Bachelier visits the New York Stock Exchange. Bachelier's scale for stock prices. Volatility. Fractal sums of random variables. Some fun with logistic art. Julia sets.

Prechter's drum roll. Symmetric stable distributions and the gold mean law. The Fibonacci dynamical system.

Grow brain. Hurst, hydrology, and the annual flooding of the Nile. Calculating the Hurst exponent. A misunderstanding to avoid. Bull and bear markets.

The Correlation Integral and the Correlation Dimension.

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