Multidimensional stochastic liquidity in Kyle’s model of informed trading
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摘要
This paper develops a variational formulation of Kyle’s model with stochastic liquidity and multiple assets, introducing a matrix-valued martingale depth that generates a linear-Gaussian equilibrium with a matrix-valued price impact under the martingale dual condition (MDC). The insider’s information release speed is determined endogenously via a primal–dual optimization problem inspired by causal optimal transport, and MDC requires the dual optimizer to be a true martingale for equilibrium existence. The scalar and common-eigenbasis cases verify the construction, while the fully general matrix-valued setting leads to a coupled matrix forward–backward system. As a byproduct, a matrix-valued Doob–Meyer decomposition for submartingales is established. [page::1]
