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Minimal Variance Hedging For Insider Trading

Author

Listed:
  • FRANCESCA BIAGINI

    (Department of Mathematics, LMU, Theresienstr. 39, D-80333 Munich, Germany)

  • BERNT ØKSENDAL

    (Center of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, Box 1053, Blindern, N-0316 Oslo, Norway;
    Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway)

Abstract

In this paper, we first study the problem of minimal hedging for an insider trader in incomplete markets. We use the forward integral in order to model the insider portfolio and consider a general larger filtration. We characterize the optimal strategy in terms of a martingale condition. In the second part we focus on a problem of mean-variance hedging where the insider tries to minimize the variance of his wealth at time T given that this wealth has a fixed expected value A. We solve this problem for an initial enlargement of filtration by providing an explicit solution.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:08:n:s0219024906003998
    DOI: 10.1142/S0219024906003998
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    References listed on IDEAS

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    1. Arturo Kohatsu-Higa & Agnès Sulem, 2006. "A Large Trader-Insider Model," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 3, pages 101-124, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. José Manuel Corcuera & Giulia Nunno & José Fajardo, 2019. "Kyle equilibrium under random price pressure," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 77-101, June.
    2. David B. Colwell & Nadima El‐Hassan & Oh Kang Kwon, 2021. "Variance minimizing strategies for stochastic processes with applications to tracking stock indices," International Review of Finance, International Review of Finance Ltd., vol. 21(2), pages 430-446, June.
    3. H'el`ene Halconruy, 2021. "The insider problem in the trinomial model: a discrete-time jump process approach," Papers 2106.15208, arXiv.org, revised Sep 2023.
    4. José Manuel Corcuera & Giulia Di Nunno, 2018. "Kyle–Back’S Model With A Random Horizon," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-41, March.
    5. Albina Danilova, 2016. "Stock Market Insider Trading in Continuous Time with Imperfect Dynamic Information," Papers 1607.00035, arXiv.org.
    6. Markus Hess, 2018. "Pricing Temperature Derivatives Under Weather Forecasts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-34, August.
    7. George Bouzianis & Lane P. Hughston, 2020. "Optimal Hedging in Incomplete Markets," Papers 2006.12989, arXiv.org, revised Sep 2020.

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