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Multidimensional stochastic liquidity in Kyle's model of informed trading

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  • Ibrahim Ekren
  • Evangelos A. Nikitopoulos
  • Lu Vy

Abstract

We develop a variational formulation of Kyle's model of informed trading that accommodates stochastic liquidity and multiple traded assets. The main equilibrium result is stated first: under a martingale dual condition, a matrix-valued martingale depth process generates a linear-Gaussian equilibrium with stochastic matrix-valued price impact. We derive this martingale from a primal-dual problem, inspired by causal optimal transport, that characterizes the endogenous speed at which the insider injects private information into prices; in general, this problem admits only local martingale optimizers, and the martingale dual condition is the hypothesis that the optimizer is a true martingale. We interpret informed trading as the optimal liquidation of private information and verify the construction in the scalar and common-eigenbasis cases. The fully general matrix-valued case reduces to a coupled matrix FBSDE, which we isolate as the remaining obstruction. Along the way, we establish an independently interesting Doob-Meyer decomposition for general (not necessarily symmetric) matrix-valued submartingales.

Suggested Citation

  • Ibrahim Ekren & Evangelos A. Nikitopoulos & Lu Vy, 2026. "Multidimensional stochastic liquidity in Kyle's model of informed trading," Papers 2607.10934, arXiv.org.
    • Handle: RePEc:arx:papers:2607.10934
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    References listed on IDEAS

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    1. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    2. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    3. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    4. Ibrahim Ekren & Brad Mostowski & Gordan Žitković, 2025. "Kyle’s model with stochastic liquidity," Finance and Stochastics, Springer, vol. 29(4), pages 1195-1231, October.
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