Kyle meets time-inconsistency: a dynamic mean--variance informed trading problem
Abstract
We study a Kyle--Back model in which the informed trader has dynamic mean--variance preferences, leading to a time-inconsistent trading problem that is formulated as an intrapersonal game. The model combines two equilibrium requirements: a trading--pricing equilibrium between the informed trader and the market maker, and a time-consistent equilibrium among the trader's successive selves. Following the framework of Cho (2003), we consider both risk-neutral and risk-averse informed traders. In the risk-neutral case, we derive the equilibrium trading strategy and price impact explicitly. In the risk-averse case, we establish existence and characterize the equilibrium through a coupled system of nonlinear ordinary differential equations. Our main technique is to reduce the equilibrium conditions to a forward--backward ODE system and resolve the resulting boundary conditions by a shooting argument. Economically, the mean--variance preference reshapes the intertemporal trade-off between exploiting current private information and preserving future informational advantage, generating a declining term structure of price impact and shifting both information revelation and informed-trading profits toward earlier stages of the trading horizon.
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BibTeX
@misc{deng2026kyle,
title = {{Kyle meets time-inconsistency: a dynamic mean--variance informed trading problem}},
author = {Shuoqing Deng and Zhichao Luo and Zhenhua Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38701},
eprint = {2609.38701},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38701},
}
RIS
TY - UNPB
TI - Kyle meets time-inconsistency: a dynamic mean--variance informed trading problem
AU - Shuoqing Deng
AU - Zhichao Luo
AU - Zhenhua Wang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38701
UR - https://arxiv.org/abs/2609.38701
AB - We study a Kyle--Back model in which the informed trader has dynamic mean--variance preferences, leading to a time-inconsistent trading problem that is formulated as an intrapersonal game. The model combines two equilibrium requirements: a trading--pricing equilibrium between the informed trader and the market maker, and a time-consistent equilibrium among the trader's successive selves. Following the framework of Cho (2003), we consider both risk-neutral and risk-averse informed traders. In the risk-neutral case, we derive the equilibrium trading strategy and price impact explicitly. In the risk-averse case, we establish existence and characterize the equilibrium through a coupled system of nonlinear ordinary differential equations. Our main technique is to reduce the equilibrium conditions to a forward--backward ODE system and resolve the resulting boundary conditions by a shooting argument. Economically, the mean--variance preference reshapes the intertemporal trade-off between exploiting current private information and preserving future informational advantage, generating a declining term structure of price impact and shifting both information revelation and informed-trading profits toward earlier stages of the trading horizon.
ER -