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Dynamic Markov bridges motivated by models of insider trading

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  • Luciano Campi
  • Umut c{C}etin
  • Albina Danilova

Abstract

Given a Markovian Brownian martingale $Z$, we build a process $X$ which is a martingale in its own filtration and satisfies $X_1 = Z_1$. We call $X$ a dynamic bridge, because its terminal value $Z_1$ is not known in advance. We compute explicitly its semimartingale decomposition under both its own filtration $\cF^X$ and the filtration $\cF^{X,Z}$ jointly generated by $X$ and $Z$. Our construction is heavily based on parabolic PDE's 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 Back and Pedersen's \cite{BP}, where insider's additional information evolves over time.

Suggested Citation

  • Luciano Campi & Umut c{C}etin & Albina Danilova, 2012. "Dynamic Markov bridges motivated by models of insider trading," Papers 1202.2980, arXiv.org.
  • Handle: RePEc:arx:papers:1202.2980
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    References listed on IDEAS

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    1. 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.
    2. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    3. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    4. Back, Kerry, 1992. "Insider Trading in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
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