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Point process bridges and weak convergence of insider trading models

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  • Cetin, Umut
  • Xing, Hao

Abstract

We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time $1$ value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its associated optimal trading strategy for the insider. In the equilibrium the insider employs a mixed strategy to randomly submit two types of orders: one type trades in the same direction as noise trades while the other cancels some of the noise trades by submitting opposite orders when noise trades arrive. The construction also allows us to prove that Glosten-Milgrom equilibria converge weakly to Kyle-Back equilibrium, without the additional assumptions imposed in K. Back and S. Baruch, Econometrica, 72 (2004), pp. 433-465, when the common intensity of the Poisson processes tends to infinity.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:48745
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    File URL: http://eprints.lse.ac.uk/48745/
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    References listed on IDEAS

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    1. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    2. Kohatsu-Higa, Arturo & Yamazato, Makoto, 2008. "Enlargement of filtrations with random times for processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1136-1158, July.
    3. Campi, Luciano & Cetin, Umut & Danilova, Albina, 2011. "Dynamic Markov bridges motivated by models of insider trading," LSE Research Online Documents on Economics 31538, London School of Economics and Political Science, LSE Library.
    4. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    5. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    6. Campi, Luciano & Çetin, Umut & Danilova, Albina, 2011. "Dynamic Markov bridges motivated by models of insider trading," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 534-567, March.
    7. Athreya, Krishna B., 1987. "Modified Bessel function asymptotics via probability," Statistics & Probability Letters, Elsevier, vol. 5(5), pages 325-327, August.
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    Citations

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    Cited by:

    1. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Jul 2024.
    2. Cheng Li & Hao Xing, 2013. "Asymptotic Glosten Milgrom equilibrium," Papers 1310.4994, arXiv.org, revised Jan 2015.
    3. Fabrice Baudoin & Oleksii Mostovyi, 2024. "The indifference value of the weak information," Papers 2408.02137, arXiv.org.
    4. Li, Cheng & Xing, Hao, 2015. "Asymptotic Glosten-Milgrom equilibrium," LSE Research Online Documents on Economics 60579, London School of Economics and Political Science, LSE Library.
    5. Luke M. Bennett & Wei Hu, 2023. "Filtration enlargement‐based time series forecast in view of insider trading," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 112-140, February.
    6. Umut c{C}et{i}n, 2018. "Mathematics of Market Microstructure under Asymmetric Information," Papers 1809.03885, arXiv.org.

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    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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