策略性指数调整：微分博弈、闭环均衡与均值场动力学

中文摘要 AI 辅助

我们研究在连续时间、多资产博弈中围绕指数调整的策略性交易，该博弈具有瞬态跨资产价格冲击以及关于未来指数成分的异质信念。机会主义交易者在公开公告前建仓，根据公布的成分调整头寸，并围绕遵循预定执行计划的指数基金进行交易。在无价格操纵条件下，我们在每个有限时域上构造了子博弈完美纳什均衡。仿射反馈策略通过非标准矩阵Riccati方程和线性常微分方程组计算，其数量和维度不随交易者数量增长。总库存和价格冲击仅通过总体平均信念依赖于信念，而信念差异影响个体库存头寸。在均值场标度下，我们构造了均值场均衡，并获得定量收敛和近似纳什界。数值示例表明，竞争和冲击衰减如何决定预期交易造成的不利价格偏移与指数基金在执行期间机会主义者逆其订单交易时执行成本节省之间的平衡。

英文摘要

We study strategic trading around index reconstitution in a continuous-time, multiasset game with transient cross-asset price impact and heterogeneous beliefs about future index membership. Opportunistic traders position before a public announcement, adjust to the revealed composition, and trade around an indexer following a prescribed execution schedule. Under a no-price-manipulation condition, we construct a subgame-perfect Nash equilibrium on every finite horizon. The affine feedback policies are computed from a non-standard matrix Riccati equation and linear ordinary differential equations whose number and dimensions do not grow with the number of traders. Aggregate inventories and price impact depend on beliefs only through the population-average belief, while differences in beliefs affect individual inventory positions. Under mean-field scaling, we construct a mean-field equilibrium and obtain quantitative convergence and approximate-Nash bounds. Numerical illustrations show how competition and impact decay determine the balance between adverse price displacement from anticipatory trading and savings in the indexer's execution costs when opportunists trade against its orders during implementation.

发表机构

• Institute for Computational and Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）
• Department of Management Science and Engineering, Stanford University（斯坦福大学管理科学与工程系）

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