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5491Two-Round Opportunity Value 1In round 1, a quote has fill probability 0.3 and edge 0.02 if filled. If it does not fill, you get a round-2 opportunity with fill probability 0.25 and edge 0.028. Assume a round-1 fill ends the game because your risk limit is used up. What is total expected edge?金融与交易中等数值题未尝试面试订阅5496Fill With Carry Cost 1Round 1 has fill probability 0.32 and edge 0.024, but a round-1 fill also creates carry cost 0.006 before the next decision point. If round 1 does not fill, round 2 has fill probability 0.28 and edge 0.02. What is total expected edge?金融与交易中等数值题未尝试面试订阅5501Choose First-Round Policy 1Policy A has round-1 fill probability 0.42, round-1 edge 0.012, and continuation value 0.009 if unfilled. Policy B has round-1 fill probability 0.25, round-1 edge 0.024, and continuation value 0.015 if unfilled. Which policy has higher expected value?金融与交易中等数值题未尝试面试订阅5506Two-Round Signal Tree 1Round 1 has fill probability 0.28 and edge 0.02. If round 1 does not fill, round 2 begins. At round 2 a strong signal arrives with probability 0.4; under a strong signal the quote has fill probability 0.35 and edge 0.03, while under a weak signal the fill probability is 0.2 and edge is 0.012. What is total expected edge?金融与交易困难数值题未尝试面试订阅5511Why Future Opportunity Is Part Of The Quote DecisionWhy can a quote with slightly lower immediate edge still be better once future opportunity is considered?金融与交易中等essay未尝试面试订阅5512Why Early Fill Is Not Always GoodWhy is an early fill not automatically good news in a multi-round market-making problem?金融与交易中等essay未尝试面试订阅5513Why Path Dependence MattersWhy can two strategies with the same average one-period edge have different multi-round values?金融与交易中等essay未尝试面试订阅5514Why Risk Limits Change The First QuoteWhy do tight inventory or capital limits make the first quote in a sequence more selective?金融与交易中等essay未尝试面试订阅5515Why Multi-Round Policies Need SimulationWhy is backtesting a multi-round quoting policy usually more naturally done path by path instead of only through average per-quote metrics?金融与交易中等essay未尝试面试订阅5821Expected Fills Over Many RoundsYou post the same two-sided quote in each of 8 independent rounds. In every round the quote fills with probability 0.35, and there is no inventory limit so fills do not interact. What is the expected number of fills over the 8 rounds?金融与交易简单数值题未尝试免费5822Cumulative PnL With Inventory CarryoverOver 3 rounds you quote to buy 1 unit each round when filled. Round 1 fills at price 100, round 2 fills at price 101, round 3 does not fill. After round 3 the unit is marked at fair value 102. Each unit also costs 0.10 in carry per round it is held to the end of round 3. What is total expected PnL, counting markup minus total carry?金融与交易中等数值题未尝试面试订阅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