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Random optimization on random sets

Author

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  • Emmanuel Lepinette

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

Abstract

Random sets and random preorders naturally appear in financial market modeling with transaction costs. In this paper, we introduce and study a concept of essential minimum for a family of vector-valued random variables, as a set of minimal elements with respect to some random preorder. We provide some conditions under which the essential minimum is not empty and we present two applications in optimisation for mathematical finance and economics.

Suggested Citation

  • Emmanuel Lepinette, 2020. "Random optimization on random sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 159-173, February.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:1:d:10.1007_s00186-019-00686-6
    DOI: 10.1007/s00186-019-00686-6
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    References listed on IDEAS

    as
    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. Julien Baptiste & Laurence Carassus & Emmanuel L'epinette, 2018. "Pricing without martingale measure," Papers 1807.04612, arXiv.org, revised May 2019.
    3. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    4. repec:dau:papers:123456789/5630 is not listed on IDEAS
    5. Zachary Feinstein & Birgit Rudloff, 2015. "Multi-portfolio time consistency for set-valued convex and coherent risk measures," Finance and Stochastics, Springer, vol. 19(1), pages 67-107, January.
    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.
    7. Andreas Löhne & Birgit Rudloff, 2014. "An Algorithm For Calculating The Set Of Superhedging Portfolios In Markets With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-33.
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    Cited by:

    1. Antonio Avilés López & José Miguel Zapata García, 2020. "Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations," Mathematics, MDPI, vol. 8(10), pages 1-23, October.
    2. Tahir Choulli & Emmanuel Lepinette, 2024. "Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon," Papers 2401.05713, arXiv.org.

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