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Additional logarithmic utility of an insider


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  • Amendinger, Jürgen
  • Imkeller, Peter
  • Schweizer, Martin
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    In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor's portfolio decisions are based on a public information flow, the insider possesses from the beginning extra information about the outcome of some random variable G, e.g., the future price of a stock. We solve the two optimization problems explicitly and rewrite the insider's additional expected logarithmic utility in terms of a relative entropy. This allows us to provide simple conditions on G for the finiteness of this additional utility and to show that it is basically given by the entropy of G. --

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    Bibliographic Info

    Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1998,25.

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    Date of creation: 1998
    Date of revision:
    Handle: RePEc:zbw:sfb373:199825

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    Keywords: insider trading; entropy; utility maximization; initial enlargement of filtrations; relative entropy;


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    Cited by:
    1. Ashkan Nikeghbali & Eckhard Platen, 2008. "On Honest Times in Financial Modeling," Research Paper Series 229, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Baudoin, Fabrice, 0. "Conditioned stochastic differential equations: theory, examples and application to finance," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 109-145, July.
    3. Dufresne, Pierre Collin & Hugonnier, Julien, 2007. "Pricing and hedging in the presence of extraneous risks," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 742-765, June.
    4. Buckley, Winston S. & Brown, Garfield O. & Marshall, Mario, 2012. "A mispricing model of stocks under asymmetric information," European Journal of Operational Research, Elsevier, vol. 221(3), pages 584-592.
    5. Buckley, Winston & Long, Hongwei & Perera, Sandun, 2014. "A jump model for fads in asset prices under asymmetric information," European Journal of Operational Research, Elsevier, vol. 236(1), pages 200-208.
    6. Paolo Guasoni, 2006. "Asymmetric Information in Fads Models," Finance and Stochastics, Springer, vol. 10(2), pages 159-177, April.
    7. Grzegorz Hara\'nczyk & Wojciech S{\l}omczy\'nski & Tomasz Zastawniak, 2007. "Relative and Discrete Utility Maximising Entropy," Papers 0709.1281,
    8. Peter Imkeller & Nicolas Perkowski, 2011. "The Existence of Dominating Local Martingale Measures," Papers 1111.3885,, revised Mar 2013.
    9. 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.
    10. 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.
    11. Stefan Ankirchner, 2005. "Utility duality under additional information: conditional measures versus filtration enlargements," SFB 649 Discussion Papers SFB649DP2005-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    13. El Otmani, Mohamed, 2009. "BSDEs driven by Lévy process with enlarged filtration and applications in finance," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 44-49, January.
    14. Stefan Ankirchner & Steffen Dereich & Peter Imkeller, 2005. "The Shannon Information of Filtrations and the Additional Logarithmic Utility of Insiders," SFB 649 Discussion Papers SFB649DP2005-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.


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