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5823金融与交易困难数值题medium

Optimal Skew After A Fill

题目

After a round-1 buy fill leaves you long 1 unit, you choose a round-2 quote skew s (in cents) that shifts both quotes down to encourage a sell. Selling probability is 0.3 + 0.1*s and expected edge per sell is 0.05 - 0.01*s, for s between 0 and 5. Round-2 expected edge is (selling probability)*(edge). Which integer s in {0,1,2,3,4,5} maximizes round-2 expected edge?

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