#stochastic-finance

13 June 2026 · 31 min
Price Formation in the Order Book
The models built on the order book mechanism. The efficient price is a martingale, the bounce and adverse selection set spreads, queue position sets fills, imbalance sets the microprice, Kyle's lambda turns information into impact, and Almgren-Chriss solves execution.
02 June 2026 · 7 min
Statistical Arbitrage
A complete construction of statistical arbitrage. We prove arbitrage is measure-class invariant, prove the finite fundamental theorem by separation, then prove an i.i.d. sufficient condition and locate statistical arbitrage in the gap the fundamental theorem leaves open.