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Asymptotic Glosten Milgrom equilibrium

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  • Cheng Li
  • Hao Xing

Abstract

This paper studies the Glosten Milgrom model whose risky asset value admits an arbitrary discrete distribution. Contrast to existing results on insider's models, the insider's optimal strategy in this model, if exists, is not of feedback type. Therefore a weak formulation of equilibrium is proposed. In this weak formulation, the inconspicuous trade theorem still holds, but the optimality for the insider's strategy is not enforced. However, the insider can employ some feedback strategy whose associated expected profit is close to the optimal value, when the order size is small. Moreover this discrepancy converges to zero when the order size diminishes. The existence of such a weak equilibrium is established, in which the insider's strategy converges to the Kyle optimal strategy when the order size goes to zero.

Suggested Citation

  • Cheng Li & Hao Xing, 2013. "Asymptotic Glosten Milgrom equilibrium," Papers 1310.4994, arXiv.org, revised Jan 2015.
    • Handle: RePEc:arx:papers:1310.4994
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    References listed on IDEAS

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    1. 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.
    2. Luciano Campi & Umut Çetin & Albina Danilova, 2013. "Equilibrium model with default and dynamic insider information," Finance and Stochastics, Springer, vol. 17(3), pages 565-585, July.
    3. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    4. Cetin, Umut & Xing, Hao, 2013. "Point process bridges and weak convergence of insider trading models," LSE Research Online Documents on Economics 48745, London School of Economics and Political Science, LSE Library.
    5. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    6. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
    7. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    8. repec:dau:papers:123456789/4436 is not listed on IDEAS
    9. repec:dau:papers:123456789/6880 is not listed on IDEAS
    10. Umut c{C}etin & Hao Xing, 2012. "Point process bridges and weak convergence of insider trading models," Papers 1205.4358, arXiv.org, revised Jan 2013.
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