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Insider trading in discrete time Kyle games

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  • Christoph Kuhn
  • Christopher Lorenz

Abstract

We present a discrete time version of Kyle's (1985) classic model of insider trading. The model has three kinds of traders: an insider, random noise traders, and a market maker. The insider aims to exploit her informational advantage and maximise expected profits while the market maker observes the total order flow and sets prices accordingly. First, we show how the multi-period model with finitely many pure strategies can be reduced to a (static) social system in the sense of Debreu (1952) and prove the existence of a sequential Kyle equilibrium, following Kreps and Wilson (1982). This requires no probabilistic restrictions on the true value, the insider's dynamic information, and the noise trader's actions. In the single-period model we establish bounds for the insider's strategy in equilibrium. Finally, we prove the existence of an equilibrium for the game with a continuum of actions, by considering an approximating sequence of games with finitely many actions. Because of the lack of compactness of the set of measurable price functions, standard infinite-dimensional fixed point theorems are not applicable.

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  • Christoph Kuhn & Christopher Lorenz, 2023. "Insider trading in discrete time Kyle games," Papers 2312.00904, arXiv.org.
    • Handle: RePEc:arx:papers:2312.00904
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    References listed on IDEAS

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    1. Jean-Charles Rochet & Jean-Luc Vila, 1994. "Insider Trading without Normality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 131-152.
    2. Luciano Campi & Umut Çetin, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Finance and Stochastics, Springer, vol. 11(4), pages 591-602, October.
    3. Umut Çetin, 2018. "Financial equilibrium with asymmetric information and random horizon," Finance and Stochastics, Springer, vol. 22(1), pages 97-126, January.
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    6. Umut Cetin & Kasper Larsen, 2023. "Is Kyle's equilibrium model stable?," Papers 2307.09392, arXiv.org, revised Jul 2023.
    7. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    8. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
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    11. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    12. Çetin, Umut, 2018. "Financial equilibrium with asymmetric information and random horizon," LSE Research Online Documents on Economics 84495, London School of Economics and Political Science, LSE Library.
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