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Dynamic Markov bridges motivated by models of insider trading

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  • Campi, Luciano
  • Çetin, Umut
  • Danilova, Albina

Abstract

Given a Markovian Brownian martingale Z, we build a process X which is a martingale in its own filtration and satisfies X1=Z1. We call X a dynamic bridge, because its terminal value Z1 is not known in advance. We compute its semimartingale decomposition explicitly under both its own filtration and the filtration jointly generated by X and Z. Our construction is heavily based on parabolic partial differential equations and filtering techniques. As an application, we explicitly solve an equilibrium model with insider trading that can be viewed as a non-Gaussian generalization of the model of Back and Pedersen (1998) [3], where the insider's additional information evolves over time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:3:p:534-567
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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. Back, Kerry, 1992. "Insider Trading in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    3. Föllmer, Hans & Wu, Ching-Tang & Yor, Marc, 1999. "Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 137-164, November.
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    Citations

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    Cited by:

    1. Cetin, Umut, 2019. "Linear inverse problems for Markov processes and their regularisation," LSE Research Online Documents on Economics 102633, London School of Economics and Political Science, LSE Library.
    2. Sottinen, Tommi & Yazigi, Adil, 2014. "Generalized Gaussian bridges," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3084-3105.
    3. 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.
    4. Mengütürk, Levent Ali, 2018. "Gaussian random bridges and a geometric model for information equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 465-483.
    5. Shreya Bose & Ibrahim Ekren, 2020. "Kyle-Back Models with risk aversion and non-Gaussian Beliefs," Papers 2008.06377, arXiv.org, revised Oct 2022.
    6. 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.
    7. José Manuel Corcuera & Giulia Di Nunno, 2018. "Kyle–Back’S Model With A Random Horizon," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-41, March.
    8. 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.
    9. Dolinsky, Yan & Zouari, Jonathan, 2021. "The value of insider information for super-replication with quadratic transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 394-416.
    10. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Dec 2023.
    11. Jos'e Manuel Corcuera & Giulia Di Nunno & Gergely Farkas & Bernt {O}ksendal, 2014. "A continuous auction model with insiders and random time of information release," Papers 1411.2835, arXiv.org, revised Mar 2018.
    12. 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.
    13. Cetin, Umut & Danilova, Albina, 2021. "On pricing rules and optimal strategies in general Kyle-Back models," LSE Research Online Documents on Economics 113003, London School of Economics and Political Science, LSE Library.
    14. 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.
    15. Umut c{C}etin, 2016. "Financial equilibrium with asymmetric information and random horizon," Papers 1603.08828, arXiv.org, revised Sep 2017.
    16. Luciano Campi & Umut Cetin & Albina Danilova, 2011. "Equilibrium model with default and insider's dynamic information," Working Papers hal-00613216, HAL.
    17. Ibrahim Ekren & Brad Mostowski & Gordan v{Z}itkovi'c, 2022. "Kyle's Model with Stochastic Liquidity," Papers 2204.11069, arXiv.org.
    18. Shreya Bose & Ibrahim Ekren, 2021. "Multidimensional Kyle-Back model with a risk averse informed trader," Papers 2111.01957, arXiv.org.
    19. Umut c{C}etin & Albina Danilova, 2018. "On pricing rules and optimal strategies in general Kyle-Back models," Papers 1812.07529, arXiv.org, revised Aug 2021.
    20. Umut Çetin, 2018. "Financial equilibrium with asymmetric information and random horizon," Finance and Stochastics, Springer, vol. 22(1), pages 97-126, January.
    21. Umut c{C}et{i}n, 2018. "Mathematics of Market Microstructure under Asymmetric Information," Papers 1809.03885, arXiv.org.

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