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Financial Markets with Asymmetric Information: Information Drift, Additional Utility and Entropy

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Stefan Ankirchner

    (Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany)

  • Peter Imkeller

    (Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany)

Abstract

We review a general mathematical link between utility and information theory appearing in a simple financial market model with two kinds of small investors: insiders, whose extra information is stored in an enlargement of the less informed agents' filtration. The insider's expected logarithmic utility increment is described in terms of the information drift, i.e. the drift one has to eliminate in order to perceive the price dynamics as a martingale from his perspective. We describe the information drift in a very general setting by natural quantities expressing the conditional laws of the better informed view of the world. This on the other hand allows to identify the additional utility by entropy related quantities known from information theory.

Suggested Citation

  • Stefan Ankirchner & Peter Imkeller, 2007. "Financial Markets with Asymmetric Information: Information Drift, Additional Utility and Entropy," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 1, pages 1-21, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812770448_0001
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    Citations

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    Cited by:

    1. Monique Jeanblanc & Libo Li & Shiqi Song, 2018. "An enlargement of filtration formula with applications to multiple non-ordered default times," Finance and Stochastics, Springer, vol. 22(1), pages 205-240, January.
    2. Olfa Draouil & Bernt {O}ksendal, 2018. "Viable Insider Markets," Papers 1801.03720, arXiv.org.
    3. Buckley, Winston S. & Long, Hongwei, 2015. "A discontinuous mispricing model under asymmetric information," European Journal of Operational Research, Elsevier, vol. 243(3), pages 944-955.

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