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From Alpha to Execution: Trading Horizons, Regimes, and Schedules under Concave Impact and Hurst Scaling

Dnyanesh Kulkarni, Revant Nayar · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.23749 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

经典的运行时间表是平板的Beta模式,它是否假定了线性影响,散发成本,和一个异常的地平线。我们研究执行在长效功法影响和Hurst尺寸的价格波动下,并做出两个贡献。首先,我们选择执行地平线,最大限度地提高交易成本实现P&L的Sharpe比率。在执行窗口期间的价格移动是P&L的一部分,所以在结构先行范围内更缓慢地减少其波动差距,因为冲击是H$,它也可以降低每股成本。(ii)紧急情况只能从Alpha实现,而命令正在工作。问题是由前面的10个数量的迹象所支配的:(i)最大时间弹性冲击$a$,这在结构先行范围内等于冲击持续差距

Machine translation (Meta M2M100); the English original follows.

Abstract

Classical execution models assume linear impact, diffusive prices, and an exogenous horizon. We study execution under concave power-law impact and Hurst-scaled price fluctuations, and make two contributions. First, we choose the execution horizon by maximizing the Sharpe ratio of the trade's realized P&L. Price moves during the execution window are part of that P&L, so executing more slowly reduces its variance, and because impact is concave it can also lower cost per share. Urgency comes only from alpha realized while the order is being worked. The problem is governed by the signs of two quantities: (i) the duration elasticity of impact $a$, which under a structural prior equals the impact-persistence gap $β- H$ and can take either sign; and (ii) the net urgency $ν$, the rate of alpha realization net of exposure relief. When $ν$ keeps its sign over the window, an interior optimum exists, to leading order in $T/t_f$, only when both are positive; otherwise the order should be worked at the fastest or slowest admissible pace. In the interior regime the first-order condition involves no impact coefficient, order size or volume, and the objective is flat: for a large-cap example, the window within 1% of maximal Sharpe spans more than an order of magnitude. Second, given the window, we derive the schedule shape by convex programming under an envelope cost. For any increasing per-share cost of delay $w(t)$, the KKT solution is $ϕ\propto (λ- w(t))_+^{1/β}$. For a Hurst-scaled envelope $w \propto t^H$, the normalized schedule depends only on $(β, H)$, has a closed form via the incomplete beta function, is front-loaded, and tapers smoothly to zero, saving 10-17% of envelope cost relative to a constant-rate (TWAP) schedule of equal duration. Whether it uses the whole window depends on a single dimensionless robustness level, for which we give a calibration.

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Topics: Regular polygon, Mathematical optimization, Mathematics, Scaling, Scheduling (production processes), Schedule

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