IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v49y2013i6p478-487.html
   My bibliography  Save this article

Essential supremum with respect to a random partial order

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406813000669
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2013.07.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Philippe Bich & Rida Laraki, 2017. "Externalities in Economies with Endogenous Sharing Rules," PSE-Ecole d'économie de Paris (Postprint) halshs-01437507, HAL.
    3. McClellon, Morgan, 2016. "Confidence models of incomplete preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 30-34.
    4. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
    5. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    6. Shaofang Qi, 2016. "A characterization of the n-agent Pareto dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 695-706, March.
    7. Attila Ambrus & Kareen Rozen, 2015. "Rationalising Choice with Multi‐self Models," Economic Journal, Royal Economic Society, vol. 125(585), pages 1136-1156, June.
    8. Marcus Pivato, 2020. "Subjective expected utility with a spectral state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 249-313, March.
    9. Karni, Edi, 2020. "Probabilistic sophistication without completeness," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 8-13.
    10. Philippe Bich & Rida Laraki, 2017. "Externalities in Economies with Endogenous Sharing Rules," Post-Print halshs-01437507, HAL.
    11. Alcantud, José Carlos R. & Dubey, Ram Sewak, 2014. "Ordering infinite utility streams: Efficiency, continuity, and no impatience," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 33-40.
    12. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    13. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2019. "Sigma-Mu efficiency analysis: A methodology for evaluating units through composite indicators," European Journal of Operational Research, Elsevier, vol. 278(3), pages 942-960.
    14. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2010. "Aggregating sets of von Neumann-Morgenstern," Documents de travail du Centre d'Economie de la Sorbonne 10068, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    15. Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
    16. Bosi, Gianni & Herden, Gerhard, 2016. "On continuous multi-utility representations of semi-closed and closed preorders," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 20-29.
    17. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    18. Asier Estevan & Roberto Maura & Oscar Valero, 2024. "Intergenerational Preferences and Continuity: Reconciling Order and Topology," Papers 2402.01699, arXiv.org.
    19. José Carlos R. Alcantud & Gianni Bosi & Magalì Zuanon, 2016. "Richter–Peleg multi-utility representations of preorders," Theory and Decision, Springer, vol. 80(3), pages 443-450, March.
    20. Dino Borie, 2020. "Finite expected multi-utility representation," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 325-331, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:49:y:2013:i:6:p:478-487. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.