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Insider information and its relation with the arbitrage condition and the utility maximization problem

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  • D'Auria, Bernardo
  • Salmerón Garrido, José Antonio

Abstract

Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of insider information. That is, we assume that, since the initial time, the information flow is altered by adding the knowledge of an additional random variable including future information. In this context we study the utility maximization problem under the logarithmic and the Constant Relative Risk Aversion (CRRA) utilities, with and without the restriction of no temporarybankruptcy. For the latter case we obtain an optimal strategy different from the one computed in [1]. We give various examples for which the insider information create arbitrage, and for which the logarithmic maximization problem is bounded or unbounded. We conclude with an interesting result, showing that the insider information may not lead to any arbitrage.

Suggested Citation

  • D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2019. "Insider information and its relation with the arbitrage condition and the utility maximization problem," DES - Working Papers. Statistics and Econometrics. WS 28805, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:28805
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    References listed on IDEAS

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    2. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1761-1784.
    3. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," LSE Research Online Documents on Economics 65150, London School of Economics and Political Science, LSE Library.
    4. 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.
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    6. Stefan Ankirchner & Steffen Dereich & Peter Imkeller, 2005. "The Shannon information of filtrations and the additional logarithmic utility of insiders," Papers math/0503013, arXiv.org, revised May 2006.
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    Cited by:

    1. Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.

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