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Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading

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  • Föllmer, Hans
  • Wu, Ching-Tang
  • Yor, Marc

Abstract

Motivated by the Kyle-Back model of "insider trading", we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition, i.e., their Doob-Meyer decomposition as semimartingales in their own filtration. In particular we characterize those transformations which generate again a Brownian motion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:1:p:137-164
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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. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    3. 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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    Cited by:

    1. Luciano Campi & Umut c{C}etin & Albina Danilova, 2012. "Dynamic Markov bridges motivated by models of insider trading," Papers 1202.2980, arXiv.org.
    2. Anne Eyraud-Loisel, 2011. "Option Hedging By An Influent Informed Investor," Post-Print hal-00450948, HAL.
    3. Campi, Luciano & Cetin, Umut & Danilova, Albina, 2013. "Explicit construction of a dynamic Bessel bridge of dimension 3," LSE Research Online Documents on Economics 45263, 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. 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.
    6. Jorge A. León & Reyla Navarro & David Nualart, 2003. "An Anticipating Calculus Approach to the Utility Maximization of an Insider," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 171-185, January.
    7. 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.
    8. Mattias Jonsson & Jan Vecer, 2005. "Insider Trading in Convergent Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(3), pages 243-252.
    9. Kiseop Lee & Seongjoo Song, 2007. "Insiders' hedging in a jump diffusion model," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 537-545.

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