发表机构
Columbia University; University of California Los Angeles（哥伦比亚大学; 加州大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究推导了随机跟踪问题的非渐近收敛速率，并将其应用于广义Obizhaeva--Wang执行模型，构造了具有相同近似速率的可实现近最优策略。
AI 中文摘要
我们研究具有绝对连续控制的一般随机目标过程的二次跟踪问题，考虑带终端约束和不带终端约束两种情况。我们基于目标的Besov型模推导显式的非渐近上界，这些上界给出了针对半鞅目标的平方根阶的精确显式速率。随后将这些结果应用于具有随机终端库存的广义Obizhaeva--Wang执行模型。我们首先开发希尔伯特空间方法来表征其最优策略，该策略包含跳跃项；为避免此类交易峰值，通过带有系数ε的二次交易率惩罚项对问题进行正则化。接着证明正则化后的最优执行成本（即正则化最优策略的超额价格冲击成本）以精确速率O(√ε)收敛。由于正则化最优策略无法以闭式形式得到，我们进一步构造了易于实现且具有相同近似速率的近最优策略。
英文摘要
We study the quadratic tracking problem of a general stochastic target process with absolutely continuous controls, with and without terminal constraint. We derive explicit, non-asymptotic upper bounds in terms of a Besov-type modulus of the target. These bounds yield sharp explicit rates that specialize to the square-root order for semimartingale targets. We then apply these results to a generalized Obizhaeva--Wang execution model with random terminal inventory. We first develop a Hilbert-space approach to characterize its optimal strategy, which includes jumps. To avoid such trading spikes, one regularizes the problem by a quadratic trading-rate penalty with coefficient $\varepsilon$. We then show that the regularized optimal execution cost---and therefore the excess price impact cost of the regularized optimal strategy---converges at the sharp rate $O(\sqrt{\varepsilon})$. Since the regularized optimal strategy is not available in closed form, we further construct a nearly optimal strategy which is readily implementable and shares the same approximation rate.
Comments44 pages, 1 figure
