Strategic Index Reconstitution: Differential Games, Closed-Loop Equilibria and Mean-Field Dynamics
Abstract
We study a continuous-time, multiasset trading game around index reconstitution, in which opportunistic traders have heterogeneous beliefs about the future index constitution and interact through transient cross-asset price impact and instantaneous execution costs. Opportunistic traders build inventory based on their individual beliefs about the future index constitution before a public announcement, adjust their positions to the revealed composition, and unwind them against the indexer's prescribed rebalancing trades at the implementation date when the new index composition takes effect. Under a no-price-manipulation condition, we construct a subgame-perfect Nash equilibrium. Its affine feedback policies are computed from a non-standard matrix Riccati equation and linear ODEs whose number and dimensions are independent of population size. Under mean-field scaling, we construct a mean-field equilibrium and obtain quantitative convergence and approximate-Nash bounds. Numerical illustrations show that greater competition among opportunists dampens price swings around implementation and that opportunistic trading lowers the indexer's implementation shortfall unless price resilience is very low. Holding the average belief fixed, greater belief dispersion can increase gross trading volume without changing net aggregate opportunist holdings or price impact.
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BibTeX
@misc{fiechtner2026strategic,
title = {{Strategic Index Reconstitution: Differential Games, Closed-Loop Equilibria and Mean-Field Dynamics}},
author = {Lukas-Benedikt Fiechtner and Jose Blanchet},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.15901},
eprint = {2609.15901},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15901},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Strategic Index Reconstitution: Differential Games, Closed-Loop Equilibria and Mean-Field Dynamics
AU - Lukas-Benedikt Fiechtner
AU - Jose Blanchet
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.15901
UR - https://arxiv.org/abs/2609.15901
AB - We study a continuous-time, multiasset trading game around index reconstitution, in which opportunistic traders have heterogeneous beliefs about the future index constitution and interact through transient cross-asset price impact and instantaneous execution costs. Opportunistic traders build inventory based on their individual beliefs about the future index constitution before a public announcement, adjust their positions to the revealed composition, and unwind them against the indexer's prescribed rebalancing trades at the implementation date when the new index composition takes effect. Under a no-price-manipulation condition, we construct a subgame-perfect Nash equilibrium. Its affine feedback policies are computed from a non-standard matrix Riccati equation and linear ODEs whose number and dimensions are independent of population size. Under mean-field scaling, we construct a mean-field equilibrium and obtain quantitative convergence and approximate-Nash bounds. Numerical illustrations show that greater competition among opportunists dampens price swings around implementation and that opportunistic trading lowers the indexer's implementation shortfall unless price resilience is very low. Holding the average belief fixed, greater belief dispersion can increase gross trading volume without changing net aggregate opportunist holdings or price impact.
ER -