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Conditional Interior and Conditional Closure of Random Sets

Author

Listed:
  • Meriam El Mansour

    (Paris Dauphine University, PSL Research University
    Faculté des Sciences de Tunis)

  • Emmanuel Lépinette

    (Paris Dauphine University, PSL Research University)

Abstract

In this paper, we introduce two new types of conditional random set taking values in a Banach space: the conditional interior and the conditional closure. The conditional interior is a version of the conditional core, as introduced by A. Truffert and recently developed by Lépinette and Molchanov, and may be seen as a measurable version of the topological interior. The conditional closure is a generalization of the notion of conditional support of a random variable. These concepts are useful for applications in mathematical finance and conditional optimization.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01768-w
    DOI: 10.1007/s10957-020-01768-w
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/12268 is not listed on IDEAS
    2. 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.
    3. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    4. repec:dau:papers:123456789/9699 is not listed on IDEAS
    5. 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.
    6. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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    Citations

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

    1. Emmanuel Lépinette & Duc Thinh Vu, 2023. "Dynamic programming principle and computable prices in financial market models with transaction costs," Post-Print hal-03284655, HAL.
    2. Dorsaf Cherif & Emmanuel Lépinette, 2023. "No-arbitrage conditions and pricing from discrete-time to continuous-time strategies," Annals of Finance, Springer, vol. 19(2), pages 141-168, June.
    3. Dorsaf Cherif & Emmanuel Lépinette, 2023. "No-arbitrage conditions and pricing from discrete-time to continuous-time strategies," Post-Print hal-03284660, HAL.
    4. Tahir Choulli & Emmanuel Lepinette, 2024. "Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon," Papers 2401.05713, arXiv.org.
    5. Meriam El Mansour & Emmanuel Lepinette, 2023. "Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty," Papers 2311.08847, arXiv.org.
    6. repec:hal:wpaper:hal-03284655 is not listed on IDEAS
    7. Dorsaf Cherif & Meriam El Mansour & Emmanuel Lepinette, 2024. "A Short Note on Super-Hedging an Arbitrary Number of European Options with Integer-Valued Strategies," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1301-1312, June.
    8. Emmanuel Lepinette & Amal Omrani, 2025. "Beyond the Leland strategies," Papers 2503.02419, arXiv.org.
    9. Laurence Carassus & Emmanuel L'epinette, 2021. "Pricing without no-arbitrage condition in discrete time," Papers 2104.02688, arXiv.org.
    10. Dorsaf Cherif & Meriam El Mansour & Emmanuel Lepinette, 2023. "A short note on super-hedging an arbitrary number of European options with integer-valued strategies," Papers 2311.08871, arXiv.org.
    11. repec:hal:wpaper:hal-03284660 is not listed on IDEAS

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