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Enlargement of filtrations with random times for processes with jumps

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  • Kohatsu-Higa, Arturo
  • Yamazato, Makoto

Abstract

We treat an extension of Jacod's theorem for initial enlargement of filtrations with respect to random times. In Jacod's theorem the main condition requires the absolute continuity of the conditional distribution of the random time with respect to a nonrandom measure. Examples appearing in the theory on insider trading require extensions of this theorem where the reference measure can be random. In this article we consider such an extension which leads to an extra term in the semimartingale decomposition in the enlarged filtration. Furthermore we consider a slightly modified enlargement which allows for the bounded variation part of the semimartingale decomposition to have finite moments depending on the modification considered. Various examples for Lévy processes are treated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:7:p:1136-1158
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    References listed on IDEAS

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    1. Axel Grorud & Monique Pontier, 1998. "Insider Trading in a Continuous Time Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 331-347.
    2. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    3. Imkeller, Peter & Pontier, Monique & Weisz, Ferenc, 2001. "Free lunch and arbitrage possibilities in a financial market model with an insider," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 103-130, March.
    4. José Corcuera & Peter Imkeller & Arturo Kohatsu-Higa & David Nualart, 2004. "Additional utility of insiders with imperfect dynamical information," Finance and Stochastics, Springer, vol. 8(3), pages 437-450, August.
    5. Arturo Kohatsu‐Higa & Agnès Sulem, 2006. "Utility Maximization In An Insider Influenced Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 153-179, January.
    6. Axel Grorud, 2000. "Asymmetric Information In A Financial Market With Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 641-659.
    7. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Cited by:

    1. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    2. 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.
    3. 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.

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