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5823Optimal Skew After A FillAfter 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?金融与交易困难数值题未尝试面试订阅5824Learning Your Fill RateYour unknown per-round fill probability is either 0.2 (prior 0.5) or 0.5 (prior 0.5). You quote 3 independent rounds and observe exactly 2 fills. What is the posterior probability that the true fill probability is 0.5?金融与交易中等数值题未尝试面试订阅5825Reprice After An Informative FillYour round-1 bid fills. A fill is more likely when an informed seller is present, so after a fill you assign probability 0.6 to fair value having dropped by 0.05 (and 0.4 to no change). In round 2 you re-quote and earn raw edge 0.04 if filled, with fill probability 0.5, but you also still hold the round-1 unit which loses the fair-value drop. What is the expected round-2 PnL including the revaluation of the held unit?金融与交易困难数值题未尝试面试订阅5826Expected Wait Until First FillYou repost the same quote every round; each round it fills independently with probability 0.2. Rounds continue indefinitely until the first fill. What is the expected number of rounds until (and including) the first fill?金融与交易简单数值题未尝试免费