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Essential supremum and essential maximum with respect to random preference relations

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  • Kabanov, Yuri
  • Lépinette, Emmanuel

Abstract

In the first part of the paper, we study concepts of supremum and maximum as subsets of a topological space X endowed by preference relations. Several rather general existence theorems are obtained for the case where the preferences are defined by countable semicontinuous multi-utility representations. In the second part of the paper, we consider partial orders and preference relations “lifted” from a metric separable space X endowed by a random preference relation to the space L0(X) of X-valued random variables. We provide an example of application of the notion of essential maximum to the problem of the minimal portfolio super-replicating an American-type contingent claim under transaction costs.

Suggested Citation

  • Kabanov, Yuri & Lépinette, Emmanuel, 2013. "Essential supremum and essential maximum with respect to random preference relations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 488-495.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:6:p:488-495
    DOI: 10.1016/j.jmateco.2013.05.007
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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. repec:dau:papers:123456789/1800 is not listed on IDEAS
    3. B. Bouchard & Yu. M. Kabanov & N. Touzi, 2001. "Option pricing by large risk aversion utility¶under transaction costs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 24(2), pages 127-136, November.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    5. 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. Jun Zhao & Emmanuel Lépinette & Peibiao Zhao, 2019. "Pricing under dynamic risk measures," Post-Print hal-02135232, HAL.
    6. Emmanuel Lepinette & Ilya Molchanov, 2017. "Conditional cores and conditional convex hulls of random sets," Papers 1711.10303, arXiv.org.
    7. Laurence Carassus & Emmanuel L'epinette, 2021. "Pricing without no-arbitrage condition in discrete time," Papers 2104.02688, arXiv.org.

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