Chaos and Fractals in
Financial Markets, Part 1

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.

Chaos and Fractals in
Financial Markets, Part 2
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.

Chaos and Fractals in
Financial Markets, Part 3
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.

Chaos and Fractals in
Financial Markets, Part 4
Gamblers, zero-sets, and fractal mountains. Futures trading
and the gambler's ruin problem. An example. Gauss versus
Cauchy. Location and scale.

Chaos and Fractals in
Financial Markets, Part 5
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.

Chaos and Fractals in
Financial Markets, Part 6
Prechter's drum roll. Symmetric stable distributions and the
gold mean law. The Fibonacci dynamical system.

Chaos and Fractals in
Financial Markets, Part 7
Grow brain. Hurst, hydrology and the annual flooding of the
Nile. Calculating the Hurst exponent. A misunderstanding to
avoid. Bull and bear markets.

These articles are parts of a work in progress. ©1999-2001 J. Orlin Grabbe. A