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The insider trading problem in a jump-binomial model

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  • Hélène Halconruy

    (Léonard de Vinci Pôle universitaire, Research Center
    Laboratoire Modal’X, Université Paris Nanterre)

Abstract

We study insider trading in a jump-binomial model of the financial market that is based on a marked binomial process and that serves as a suitable alternative to some classical trinomial models. Our investigations focus on the two main questions: measuring the advantage of the insider’s additional information and stating a closed form for her hedging strategy. Our approach is based on the results of enlargement of filtration in a discrete-time setting stated by Blanchet-Scalliet and Jeanblanc (in: From probability to finance, Springer, Berlin, 2020) and on a stochastic analysis for marked binomial processes developed in the companion paper (Halconruy in Electron J Probab 27:1–39, 2022). Our work provides in a discrete-time and an incomplete market setting the analogues of some results of Amendinger et al. (Stoch Process Appl 89(1):101–116, 2000; Finance Stoch 7(1):29–46, 2003), Imkeller et al. (1998, 2006) and extends in an insider framework some utility maximization results stated in Delbaen and Schachermayer (The mathematics of arbitrage, Springer, Berlin, 2006) and in Runggaldier et al. (in: Seminar on stochastic analysis, random fields and applications III, Springer, Berlin, 2002).

Suggested Citation

  • Hélène Halconruy, 2023. "The insider trading problem in a jump-binomial model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(2), pages 379-413, December.
    • Handle: RePEc:spr:decfin:v:46:y:2023:i:2:d:10.1007_s10203-023-00412-2
    DOI: 10.1007/s10203-023-00412-2
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Marcel Nutz, 2016. "Utility Maximization Under Model Uncertainty In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 252-268, April.
    4. 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.
    5. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    6. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    7. Francesca Biagini & Bernt Øksendal, 2006. "Minimal Variance Hedging For Insider Trading," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(08), pages 1351-1375.
    8. Hiroaki Hata & Arturo Kohatsu-Higa, 2013. "A market model with medium/long-term effects due to an insider," Quantitative Finance, Taylor & Francis Journals, vol. 13(3), pages 421-437, February.
    9. Arturo Kohatsu‐Higa & Agnès Sulem, 2006. "Utility Maximization In An Insider Influenced Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 153-179, January.
    10. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    11. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    12. Peter Imkeller, 2003. "Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 153-169, January.
    13. 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.
    14. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Insider trading; Trinomial model; Enlargement of filtrations; Malliavin’s calculus; Utility maximization;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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