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Chances for the honest in honest versus insider trading

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  • Mauricio Elizalde
  • Carlos Escudero

Abstract

We study a Black-Scholes market with a finite time horizon and two investors: an honest and an insider trader. We analyze it with anticipating stochastic calculus in two steps. First, we recover the classical result on portfolio optimization that shows that the expected logarithmic utility of the insider is strictly greater than that of the honest trader. Then, we prove that, whenever the market is viable, the honest trader can get a higher logarithmic utility, and therefore more wealth, than the insider with a strictly positive probability. Our proof relies on the analysis of a sort of forward integral variant of the Dol\'eans-Dade exponential process. The main financial conclusion is that the logarithmic utility is perhaps too conservative for some insiders.

Suggested Citation

  • Mauricio Elizalde & Carlos Escudero, 2021. "Chances for the honest in honest versus insider trading," Papers 2106.10033, arXiv.org, revised May 2022.
    • Handle: RePEc:arx:papers:2106.10033
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    References listed on IDEAS

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    1. Jorge A. León & Reyla Navarro & David Nualart, 2003. "An Anticipating Calculus Approach to the Utility Maximization of an Insider," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 171-185, January.
    2. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    3. Carlos Escudero & Sandra Ranilla-Cortina, 2020. "Optimal portfolios for different anticipating integrals under insider information," Papers 2007.02316, arXiv.org, revised Jan 2021.
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    Cited by:

    1. Mauricio Elizalde & Carlos Escudero & Tomoyuki Ichiba, 2022. "Optimal investment with insider information using Skorokhod & Russo-Vallois integration," Papers 2211.07471, arXiv.org, revised Sep 2025.
    2. Mauricio Elizalde & Carlos Escudero & Tomoyuki Ichiba, 2025. "Optimal Investment with Insider Information Using Skorokhod & Russo-Vallois Integration," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-43, December.
    3. Bernardo D'Auria & Carlos Escudero, 2024. "Time evaluation of portfolio for asymmetrically informed traders," Papers 2410.16010, arXiv.org.

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