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Local risk-minimization under transaction costs

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  • Lamberton, Damien
  • Pham, Huyên
  • Schweizer, Martin
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    Abstract

    We propose a new approach to the pricing and hedging of contingent claims under transaction costs in a general incomplete market in discrete time. Under the assumptions of a bounded mean-variance tradeoff, substantial risk and a nondegeneracy condition on the conditional variances of asset returns, we prove the existence of a locally risk-minimizing strategy inclusive of transaction costs for every square-integrable contingent claim. Then we show that local riskminimization is robust under the inclusion of transaction costs: The preceding strategy which is locally risk-minimizing inclusive of transaction costs in a model with bid-ask spreads on the underlying asset is also locally risk-minimizing without transaction costs in a fictitious model which is frictionless and where the fictitious asset price lies between the bid and ask price processes of the original model. In particular, our results apply to any nondegenerate model with a finite state space if the transaction cost parameter is sufficiently small. --

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    Bibliographic Info

    Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1998,18.

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    Date of creation: 1998
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    Handle: RePEc:zbw:sfb373:199818

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    Related research

    Keywords: option pricing; hedging; transaction costs; locally risk-minimizing strategies; mean-variance tradeoff;

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    Cited by:
    1. Jan Kallsen & Johannes Muhle-Karbe, 2011. "Existence of shadow prices in finite probability spaces," Computational Statistics, Springer, vol. 73(2), pages 251-262, April.
    2. Eric Beutner, 2007. "Mean–variance hedging under transaction costs," Computational Statistics, Springer, vol. 65(3), pages 539-557, June.
    3. Pansera, Jérôme, 2012. "Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 1-11.
    4. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    5. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the Existence of Shadow Prices," Papers 1111.6633, arXiv.org, revised Jan 2013.
    6. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2013. "On the existence of shadow prices," Finance and Stochastics, Springer, vol. 17(4), pages 801-818, October.
    8. Jin Hyuk Choi & Mihai Sirbu & Gordan Zitkovic, 2012. "Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs," Papers 1204.0305, arXiv.org, revised Jun 2012.
    9. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the existence of shadow prices," Working Papers hal-00645980, HAL.

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