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Essential supremum with respect to a random partial order

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  • Kabanov, Yuri
  • Lépinette, Emmanuel

Abstract

Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in Rd is lifted to the space L0(Rd) of d-dimensional random variables. In contrast to the classical definition, we define the essential supremum as a subset of random variables satisfying some natural properties. Applications of the introduced notion to a hedging problem under transaction costs and set-valued dynamic risk measures are given.

Suggested Citation

  • Kabanov, Yuri & Lépinette, Emmanuel, 2013. "Essential supremum with respect to a random partial order," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 478-487.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:6:p:478-487
    DOI: 10.1016/j.jmateco.2013.07.002
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    References listed on IDEAS

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    1. Bruno Bouchard & Erik Taflin, 2010. "No-arbitrage of second kind in countable markets with proportional transaction costs," Papers 1008.3276, arXiv.org, revised Feb 2013.
    2. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
    3. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
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    Citations

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    Cited by:

    1. Julien Baptiste & Laurence Carassus & Emmanuel L'epinette, 2018. "Pricing without martingale measure," Papers 1807.04612, arXiv.org, revised May 2019.
    2. Laurence Carassus, 2021. "Quasi-sure essential supremum and applications to finance," Papers 2107.12862, arXiv.org, revised Mar 2024.
    3. Mario Sikic, 2015. "Financial market models in discrete time beyond the concave case," Papers 1512.01758, arXiv.org.
    4. Meriam El Mansour & Emmanuel Lépinette, 2020. "Conditional Interior and Conditional Closure of Random Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 356-369, November.
    5. Tahir Choulli & Emmanuel Lepinette, 2024. "Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon," Papers 2401.05713, arXiv.org.
    6. Meriam El Mansour & Emmanuel Lepinette, 2023. "Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty," Papers 2311.08847, arXiv.org.
    7. Jun Zhao & Emmanuel Lépinette & Peibiao Zhao, 2019. "Pricing under dynamic risk measures," Post-Print hal-02135232, HAL.
    8. Emmanuel Lepinette & Ilya Molchanov, 2017. "Conditional cores and conditional convex hulls of random sets," Papers 1711.10303, arXiv.org.
    9. Laurence Carassus & Emmanuel L'epinette, 2021. "Pricing without no-arbitrage condition in discrete time," Papers 2104.02688, arXiv.org.
    10. Sofiane Aboura & Emmanuel Lépinette, 2013. "An Alternative Model to Basel Regulation," Working Papers hal-00825018, HAL.

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