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Leptokurtic
Finance Is Geometry, and It All Comes Back to Jensen’s Inequality
Logarithms, Kelly, ergodicity, and tail risk meet at the same geometry: wealth compounds multiplicatively, the logarithm is concave, and Jensen's inequality measures the cost of variability.
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Leptokurtic
Detecting Crashes with Fat-Tail Statistics
We built fatcrash, a Rust+Python toolkit with 15 crash detection methods: LPPLS, DFA, EVT, Hill, Kappa, Hurst, GSADF, momentum/reversal, price velocity, and more. Tested on 96 drawdowns across BTC, SPY, Gold, 23 forex pairs, and equity crises with honest precision/recall/F1 metrics. Plus: which methods transfer to revenue and profit data.
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The Edge of Chaos
When Risk Models Create Risk
The last essay said the tail is too hard to measure. Jón Daníelsson goes one step further: in finance, the measurement itself changes the thing measured. When everyone uses the same risk model, the model becomes a synchronization device. The answer is a system designed to survive without everyone trusting the same number.
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The Edge of Chaos
The Limits of Knowing
Every method in this series rests on one number: how close a system sits to its edge. Nassim Taleb spent a career arguing that this is exactly the number you cannot trust. For fat-tailed systems the data needed to pin down the tail converges too slowly, and being honest about your uncertainty fattens the tail further. This is the counterpunch, and where it leaves us.