How do you sell 1 million shares without crashing the price? Trade too fast and you move the market against yourself through market impact. Trade too slowly and you remain exposed to price risk while you still hold the position. In their 2000 paper, Almgren and Chriss formalized this problem by minimizing expected execution cost plus a risk penalty. The result is a closed-form optimal liquidation schedule. A risk-neutral trader (λ = 0) gets a simple TWAP: equal slices over time. As risk aversion

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