发表机构
Ceremade, Université Paris Dauphine-PSL（巴黎第九大学PSL研究组合数学与数据科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对市场参与者基于异质时间跨度决策、市场冲击与总头寸相关的问题，构建线性平均场模型，刻画均衡并分析极限情形下观测价格的收敛特性。
AI 中文摘要
尽管市场参与者通常可获取共同信息集，但他们基于不同时间跨度形成的预测做出决策。由于市场冲击取决于总头寸而非交易者身份，这些决策通过集体效应对价格产生反馈。我们引入此类相互作用的线性平均场模型：观测价格被分解为鞅分量、由Volterra过程表示的共同可预测信号，以及总头寸产生的市场冲击。代理人根据未来信号增量的条件预测，以及各自时间跨度内预期总冲击的一部分来建立头寸。在高斯- Volterra框架内，我们通过总头寸的线性不动点方程刻画均衡，并在明确条件下证明其存在性与唯一性。均衡时，我们确定平衡条件以抵消共同信号向观测价格的直接传递。随后研究代理人充分考虑市场冲击的极限情况：在满足明确条件的适当缩放均衡族中，可预测信号与市场冲击的贡献在极限下抵消，观测价格收敛至其鞅分量。对于分数型信号和Gamma分布的时间跨度，我们进一步推导局部Hölder界，并确定使观测价格具有与布朗运动相容的局部正则性的时间跨度分布。
英文摘要
Although market participants generally have access to a common information set, they make decisions based on forecasts formed over heterogeneous horizons. Because market impact depends on aggregate positions rather than trader identities, these decisions feed back into prices through their collective effect. We introduce a linear mean-field model of this interaction. The observed price is decomposed into a martingale component, a common predictable signal represented by a Volterra process, and the market impact generated by aggregate positions. Agents take positions according to conditional forecasts of future signal increments and a fraction of anticipated aggregate impact over their respective horizons. Within a Gaussian-Volterra framework, we characterize equilibrium through a linear fixed-point equation for aggregate positions and establish existence and uniqueness under explicit conditions. At equilibrium, we identify a balance condition that cancels the direct transmission of the common signal to the observed price. We then study the limit in which agents fully account for market impact. Along a suitably scaled family of equilibria satisfying explicit conditions, the contributions of the predictable signal and the market impact cancel in the limit, and the observed price converges to its martingale component. For fractional-type signals and Gamma-distributed horizons, we further derive local Hölder bounds and identify the horizon distributions for which the observed price has local regularity compatible with that of Brownian motion.
