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Robust mean–variance hedging via G-expectation

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  • Biagini, Francesca
  • Mancin, Jacopo
  • Brandis, Thilo Meyer

Abstract

In this paper we study mean–variance hedging under the G-expectation framework. Our analysis is carried out by exploiting the G-martingale representation theorem and the related probabilistic tools, in a continuous financial market with two assets, where the discounted risky one is modeled as a symmetric G-martingale. By tackling progressively larger classes of contingent claims, we are able to explicitly compute the optimal strategy under general assumptions on the form of the contingent claim.

Suggested Citation

  • Biagini, Francesca & Mancin, Jacopo & Brandis, Thilo Meyer, 2019. "Robust mean–variance hedging via G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1287-1325.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:4:p:1287-1325
    DOI: 10.1016/j.spa.2018.04.007
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    References listed on IDEAS

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    1. Osuka, Emi, 2013. "Girsanov’s formula for G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1301-1318.
    2. Soner, H. Mete & Touzi, Nizar & Zhang, Jianfeng, 2011. "Martingale representation theorem for the G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 265-287, February.
    3. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    4. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1170-1195.
    5. Martin Schweizer & HuyËn Pham & (*), Thorsten RheinlÄnder, 1998. "Mean-variance hedging for continuous processes: New proofs and examples," Finance and Stochastics, Springer, vol. 2(2), pages 173-198.
    6. R. Tevzadze & T. Uzunashvili, 2012. "Robust Mean-Variance Hedging And Pricing Of Contingent Claims In A One Period Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-9.
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    Cited by:

    1. Daniel Bartl & Ariel Neufeld & Kyunghyun Park, 2023. "Sensitivity of robust optimization problems under drift and volatility uncertainty," Papers 2311.11248, arXiv.org.

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