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5985概率简单derivationshort

Expected Total Slippage With Negative Drift

题目

A market-making desk incurs i.i.d. per-trade adverse-selection costs X1,X2,X_1,X_2,\dots with E[Xi]=0.4E[X_i]=-0.4 (a net loss per trade). The number of trades in a session, NN, is independent of the costs and is Poisson with mean 1515. Compute the expected cumulative cost E ⁣[i=1NXi]E\!\left[\sum_{i=1}^N X_i\right].

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