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中文题目A maker holds front-of-queue at half-spread 0.06, giving fill probability 0.5 with adverse loss 0.02 per fill. Alternatively it can step one tick tighter to half-spread 0.05, jumping ahead of the whole queue for fill probability 0.8, same 0.02 loss. The metric is fill_prob * (h -
打开 →A simplified venue state is (bid queue mod 6, ask queue mod 6, regime among 4 labels). How many observations force a repeated full state?
打开 →A queue length process lives on $\{0,1,2\}$. From state $0$ it stays at $0$ with probability $1-a$ and moves to $1$ with probability $a$. From state $1$ it moves to $2$ with probability $a$, to $0$ with probability $b$, and stays with probability $1-a-b$. From state $2$ it moves
打开 →Your 300-share quote reaches the front of the queue with probability 0.6. If it does, it fully fills (300 shares); otherwise the queue clears only partway and you fill just 100 shares. Net edge is 0.015 per share in both cases. What is the expected PnL of the quote, accounting fo
打开 →If you join the current best quote, fill probability is 0.26, size is 120, raw edge per share is 0.011, and rebate is 0.0005. If you improve the quote, fill probability becomes 0.18, size is 120, raw edge per share is 0.017, and rebate is 0.0005. Which action has higher expected
打开 →A quote can fill in two sizes: with probability 0.25 you trade 100 shares and earn 0.012 raw edge per share; with probability 0.1 you trade 250 shares and earn 0.009 raw edge per share. Rebate is 0.0005 per share in either case. What is expected PnL?
打开 →Five labeled tasks are independently assigned to four labeled queues. How many assignments produce queue loads that, after sorting, equal (2,2,1,0)?
打开 →You are training on a small image-like signal dataset where small translations and mirror flips preserve the label by construction. The network fits the training set too easily. What regularization lever should move to the front of the queue?
打开 →A competitor quotes half-spread 0.04. If the maker matches at 0.04 it shares the queue and wins 40% of a 0.04-edge round, with adverse loss 0.012 per fill on fills it wins; fill volume is 100 rounds. If it undercuts to 0.03 it captures 100% of fills but earns only 0.03 edge with
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