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A superhedging approach to stochastic integration

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  • Łochowski, Rafał M.
  • Perkowski, Nicolas
  • Prömel, David J.

Abstract

Using Vovk’s outer measure, which corresponds to a minimal superhedging price, the existence of quadratic variation is shown for “typical price paths” in the space of càdlàg functions possessing a mild restriction on the jumps directed downwards. In particular, this result includes the existence of quadratic variation of “typical price paths” in the space of non-negative càdlàg paths and implies the existence of quadratic variation in the sense of Föllmer quasi surely under all martingale measures. Based on the robust existence of the quadratic variation, a model-free Itô integration is developed.

Suggested Citation

  • Łochowski, Rafał M. & Perkowski, Nicolas & Prömel, David J., 2018. "A superhedging approach to stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4078-4103.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:12:p:4078-4103
    DOI: 10.1016/j.spa.2018.01.009
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Andrew L. Allan & Chong Liu & David J. Promel, 2021. "A C\`adl\`ag Rough Path Foundation for Robust Finance," Papers 2109.04225, arXiv.org, revised May 2023.
    2. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2021. "One-dimensional game-theoretic differential equations," Papers 2101.08041, arXiv.org.
    3. Lesiba Ch. Galane & Rafa{l} M. {L}ochowski & Farai J. Mhlanga, 2018. "On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales," Papers 1807.05692, arXiv.org, revised Feb 2022.
    4. Rafa{l} M. {L}ochowski, 2021. "BDG inequalities and their applications for model-free continuous price paths with instant enforcement," Papers 2109.07928, arXiv.org, revised Aug 2023.

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