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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5516Reservation Price 1A market maker uses reservation price = fair value - lambda*inventory. If fair value is 100, inventory is 50, lambda is 0.006, and the chosen half-spread is 0.02, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5517Reservation Price 2A market maker uses reservation price = fair value - lambda*inventory. If fair value is 50, inventory is -80, lambda is 0.004, and the chosen half-spread is 0.015, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5518Reservation Price 3A market maker uses reservation price = fair value - lambda*inventory. If fair value is 75.5, inventory is 120, lambda is 0.003, and the chosen half-spread is 0.018, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5519Reservation Price 4A market maker uses reservation price = fair value - lambda*inventory. If fair value is 20.1, inventory is -40, lambda is 0.008, and the chosen half-spread is 0.012, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5521Passive Unwind Versus Crossing 1You are long 300 shares. If you skew passively and wait, you fully unwind with probability 0.4 and earn 0.012 per share; if the unwind does not happen, you expect a mark-to-market loss of 0.008 per share on the remaining position. Alternatively, you can cross the spread now and pay 0.005 per share. Which action has higher expected PnL?金融与交易中等数值题未尝试面试订阅5526Required Skew 1Without skew, expected bid-fill probability is 0.32 and ask-fill probability is 0.18. If you increase ask-side skew by s, bid-fill probability becomes 0.32 - 0.02*s and ask-fill probability becomes 0.18 + 0.015*s. What is the smallest nonnegative s that makes expected inventory change no longer positive?金融与交易中等数值题未尝试面试订阅5531Expected Ending Inventory 1You start long 200 shares. If you keep both sides on, expected bid-fill probability is 0.24, ask-fill probability is 0.16, and each fill size is 50. If you instead turn the bid off and only leave the ask quote live, what expected ending inventory do you get under each policy, and which policy leaves you closer to flat?金融与交易中等数值题未尝试面试订阅5536Why Long Inventory Changes The MidWhy does holding a large long inventory typically shift a market maker's practical quote center below the estimated fair value?金融与交易中等essay未尝试面试订阅5537Why Immediate Unwind Can Be RationalWhy might a market maker rationally cross the spread to reduce inventory even though crossing is mechanically costly?金融与交易中等essay未尝试面试订阅5538Why One-Sided Quoting ExistsWhy do market makers sometimes stop quoting one side entirely instead of merely widening both sides?金融与交易中等essay未尝试面试订阅5539Why Inventory And Information Risk InteractWhy is a bad inventory state especially dangerous when adverse selection is also high?金融与交易中等essay未尝试面试订阅5540Why Inventory Policy Needs More Than Spread MathWhy is inventory management usually not solvable by one static spread formula alone?金融与交易中等essay未尝试面试订阅5751Kelly Fraction From Edge and OddsA binary bet pays net odds of 3-to-1 (you net 3 units per unit staked on a win, lose your stake on a loss). Your win probability estimate is 0.40. What full-Kelly fraction of capital should you stake?金融与交易简单数值题未尝试免费5752Even-Money Kelly FractionYou can repeatedly take an even-money bet (win 1 unit per unit staked, or lose your stake) that you believe wins with probability 0.55. What full-Kelly fraction of capital maximizes long-run growth, and what simple expression gives it for any even-money win probability p?金融与交易简单数值题未尝试免费5753Log-Growth Rate at Full KellyFor a repeatable even-money bet that wins with probability 0.60, you bet the full-Kelly fraction. What is the resulting expected log-growth rate per round (use natural log)?金融与交易中等数值题未尝试免费5754Growth Retained at Half-KellyFor a repeatable even-money bet winning with probability 0.60, full Kelly stakes 0.20 of capital. If instead you bet half-Kelly (0.10 of capital), what fraction of the full-Kelly expected log-growth rate do you retain? Give the ratio as a decimal.金融与交易中等数值题未尝试免费