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Optimal investment with insider information using Skorokhod & Russo-Vallois integration

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  • Mauricio Elizalde
  • Carlos Escudero
  • Tomoyuki Ichiba

Abstract

We study the maximization of the logarithmic utility of an insider with different anticipating techniques. Our aim is to compare the usage of the forward and Skorokhod integrals in this context with multiple assets. We show theoretically and with simulations that the Skorokhod insider always overcomes the forward insider, just the opposite of what happens in the case of risk-neutral traders. Moreover, an ordinary trader might overcome both insiders if there is a large enough negative fluctuation in the driving stochastic process that leads to a negative enough final value. Our results point to the fact that the interplay between anticipating stochastic calculus and nonlinear utilities might yield non-intuitive results from the financial viewpoint.

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  • Mauricio Elizalde & Carlos Escudero & Tomoyuki Ichiba, 2022. "Optimal investment with insider information using Skorokhod & Russo-Vallois integration," Papers 2211.07471, arXiv.org.
    • Handle: RePEc:arx:papers:2211.07471
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    References listed on IDEAS

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    1. Mauricio Elizalde & Carlos Escudero, 2021. "Chances for the honest in honest versus insider trading," Papers 2106.10033, arXiv.org, revised May 2022.
    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. 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. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107039124.
    5. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107611986.
    6. 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.
    7. 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.
    8. 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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