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Essential supremum with respect to a random partial order

Author

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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. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
    2. 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.
    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. Mario Sikic, 2015. "Financial market models in discrete time beyond the concave case," Papers 1512.01758, arXiv.org.
    3. Sofiane Aboura & Emmanuel Lépinette, 2013. "An Alternative Model to Basel Regulation," Working Papers hal-00825018, HAL.
    4. Emmanuel Lepinette & Ilya Molchanov, 2017. "Conditional cores and conditional convex hulls of random sets," Papers 1711.10303, arXiv.org.

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