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At the Core of Finance Lies Geometry. In the End, It’s All Jensen’s Inequality. At the Core of Finance Lies Geometry. In the End, It’s All Jensen’s Inequality.
35 min read Keywords:  Jensen's inequality, Kelly criterion, ergodicity economics, tail hedging, logarithms, Spitznagel, Taleb, Peters

A 400-year journey through logarithms, Kelly, ergodicity, and tail risk to show why geometry sits at the core of finance and why Jensen’s inequality ties the whole story together.

Detecting Crashes with Fat-Tail Statistics Detecting Crashes with Fat-Tail Statistics
37 min read Keywords:  fat tails, crash detection, LPPLS, extreme value theory, DFA, Hurst, Taleb, Sornette, Bouchaud, bitcoin, finance, rust, revenue, profit, momentum, volatility targeting

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.