power laws

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Markets as Reflexive Fixed Points Markets as Reflexive Fixed Points
34 min read Keywords:  markets, reflexivity, criticality, power laws, ergodicity, Soros, Mantegna, Stanley, Kelly

Markets are more than noisy aggregators of information: beliefs about prices help determine prices, which makes reflexivity a fixed-point problem with fat tails, non-ergodicity, and hysteresis.

Power Laws, Extremistan, and Non-Ergodicity Power Laws, Extremistan, and Non-Ergodicity
21 min read Keywords:  power laws, fat tails, Extremistan, non-ergodicity, Kelly, central limit theorem

Scale invariance becomes power laws; power laws move importance to extremes; extremes make averages unstable through time.

Sandpiles and Crashes: How Systems Tune Themselves to the Brink Sandpiles and Crashes: How Systems Tune Themselves to the Brink
14 min read Keywords:  self-organized criticality, sandpile model, Per Bak, power laws, avalanches, Bouchaud, efficiency, fat tails, crashes

The last essay left a loose end. Markets can sit near a critical edge where small shocks cascade, but critical points are usually finely tuned, so who keeps a market balanced there? The answer, found in a pile of sand, is that nobody does. Some systems walk to the brink on their own, and that is where their crashes come from.