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An Anticipating Calculus Approach to the Utility Maximization of an Insider

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  • Jorge A. León
  • Reyla Navarro
  • David Nualart

Abstract

In this paper we consider a financial market with an insider that has, at time t= 0, some additional information of the whole developing of the market. We use the forward integral, which is an anticipating integral, and the techniques of the Malliavin calculus so that we can take advantage of the privileged information to maximize the expected logarithmic utility from terminal wealth.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:1:p:171-185
    DOI: 10.1111/1467-9965.00012
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    References listed on IDEAS

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    1. Föllmer, Hans & Wu, Ching-Tang & Yor, Marc, 1999. "Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 137-164, November.
    2. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    3. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    4. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
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    Citations

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    Cited by:

    1. Elisa Alòs & Christian-Olivier Ewald, 2005. "A note on the Malliavin differentiability of the Heston volatility," Economics Working Papers 880, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Zhaojun Yang & Christian-Oliver Ewald & Olaf Menkens, 2011. "Pricing and hedging of Asian options: quasi-explicit solutions via Malliavin calculus," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 93-120, August.
    3. Mohamed Ben Alaya & Ahmed Kebaier & Ngoc Khue Tran, 2020. "Local asymptotic properties for Cox‐Ingersoll‐Ross process with discrete observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1401-1464, December.
    4. Elisa Alòs & Jorge A. León, 2021. "An Intuitive Introduction to Fractional and Rough Volatilities," Mathematics, MDPI, vol. 9(9), pages 1-22, April.
    5. Anne Eyraud-Loisel, 2013. "Quadratic hedging in an incomplete market derived by an influent informed investor," Post-Print hal-00450949, HAL.
    6. Edward Hoyle & Andrea Macrina & Levent A. Menguturk, 2017. "Modulated Information Flows in Financial Markets," Papers 1708.06948, arXiv.org, revised May 2020.
    7. Carlos Escudero & Sandra Ranilla-Cortina, 2020. "Optimal portfolios for different anticipating integrals under insider information," Papers 2007.02316, arXiv.org, revised Jan 2021.
    8. Christian-Oliver Ewald & Aihua Zhang, 2006. "A new technique for calibrating stochastic volatility models: the Malliavin gradient method," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 147-158.
    9. Hyungbin Park, 2021. "Influence of risk tolerance on long-term investments: A Malliavin calculus approach," Papers 2104.00911, arXiv.org.
    10. Carlos Escudero & Sandra Ranilla-Cortina, 2020. "Optimal Portfolios for Different Anticipating Integrals under Insider Information," Mathematics, MDPI, vol. 9(1), pages 1-19, December.
    11. Peng, Xingchun & Wang, Wenyuan, 2016. "Optimal investment and risk control for an insurer under inside information," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 104-116.
    12. Mauricio Elizalde & Carlos Escudero & Tomoyuki Ichiba, 2022. "Optimal investment with insider information using Skorokhod & Russo-Vallois integration," Papers 2211.07471, arXiv.org.
    13. Mengütürk, Levent Ali, 2018. "Gaussian random bridges and a geometric model for information equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 465-483.
    14. Giulia Di Nunno & Steffen Sjursen, 2013. "Information and optimal investment in defaultable assets," Papers 1312.6032, arXiv.org.
    15. Mattias Jonsson & Jan Vecer, 2005. "Insider Trading in Convergent Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(3), pages 243-252.
    16. Mauricio Elizalde & Carlos Escudero, 2021. "Chances for the honest in honest versus insider trading," Papers 2106.10033, arXiv.org, revised May 2022.

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