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中文题目You need to buy 6% of daily volume in a liquid index future by the close, and the PM is benchmarked strictly to day-long VWAP rather than arrival. Which schedule is the most natural starting point?
打开 →A utilization surcharge is c(q)=1/(2-q) on q<2. Schedule A is deterministic with Q=1. Schedule B uses Q=1/2 or 3/2 with probability 1/2 each. Compute E[c(Q)] for Schedule B and c(E[Q]) for the shared mean.
打开 →Two execution schedules have penalties phi(q_1) and phi(q_2) under a convex phi. What does Jensen say about a random 50-50 mix versus the penalty at the average size?
打开 →An execution schedule reaches total size 11 using slices of sizes 1, 2, and 5, but the large 5-lot slice may be used at most once. Order of slices does not matter. How many schedules are possible?
打开 →A learning rate decays from eta_max to eta_min over T steps using cosine annealing. What is eta_t at step t?
打开 →A learning rate warms up linearly from 0 to eta_max over T steps. Derive eta_t for step t in the warmup phase.
打开 →A signal is expected to decay within the next 20 minutes, and waiting is more expensive than crossing a bit more spread now. Should the schedule become more or less front-loaded?
打开 →A benchmarked portfolio must minimize tracking error to the official close, and the stock has deep closing-auction liquidity. Which venue or schedule component becomes especially attractive?
打开 →You need to liquidate a medium-size position over several days with no urgent alpha and strong concern about footprint. Which scheduling style is the better default: high-POV aggression or a lower-participation passive schedule?
打开 →In a thin name, why might a trader impose a strict maximum participation rate even when the order is behind schedule?
打开 →A schedule pays a quadratic cost but also faces a blow-up term as it nears a hard capacity cap. Show that f(q) = 1 q^2 + 2/(1-q) is strictly convex on q<1.
打开 →Randomizing a schedule changes the expected nonlinear penalty, not just the mean utilization. Let phi(q)=q/(1-q) on 0<=q<1. If Q is random with E[Q]=m, is E[phi(Q)] at least phi(E[Q]) or at most phi(E[Q])?
打开 →Meetings occupy half-open time intervals [(9, 12), (10, 13), (11, 15), (14, 16)]. What is the minimum number of rooms needed so that all meetings can be scheduled without overlap?
打开 →Meetings occupy half-open time intervals [(8, 10), (9, 11), (10, 12), (10, 13), (13, 15)]. What is the minimum number of rooms needed so that all meetings can be scheduled without overlap?
打开 →A schedule trades size x over time t and pays x^2/t plus a linear time charge. Show that P(x,t)=x^2/t + 2 t is convex on the domain t>0.
打开 →Before pricing a cap, what should you inspect first about the reset schedule?
打开 →Successive halving starts with 64 configurations. Compare two keep ratios over three rounds total: keep one half each round versus keep one quarter each round. How many fewer fits does the one-quarter schedule use?
打开 →Buses arrive at a stop according to a Poisson process with rate $\lambda$ (so inter-arrival times are iid $\text{Exp}(\lambda)$ with mean $1/\lambda$). You arrive at the bus stop at a uniformly random time, independent of the bus schedule. Let $L$ be the length of the inter-arriv
打开 →Why does changing slippage curves, fee schedules, or borrow assumptions after seeing backtest performance count as extra model search?
打开 →Before a scheduled announcement, the maker believes that during its quote's lifetime the market stays in a calm regime with probability 0.6 (requiring half-spread 0.02) or switches to a stressed regime with probability 0.4 (requiring half-spread 0.10). It sets a single posted hal
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