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Commonotonicity and time-consistency for Lebesgue-continuous monetary utility functions

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  • Freddy Delbaen

    (ETH Zürich
    Universität Zürich)

Abstract

It is proved that monetary utility functions that are commonotonic and time-consistent are conditional expectations. We also give additional results on atomless and conditionally atomless probability spaces. These notions describe that in a filtration, there are many new events at each time step.

Suggested Citation

  • Freddy Delbaen, 2021. "Commonotonicity and time-consistency for Lebesgue-continuous monetary utility functions," Finance and Stochastics, Springer, vol. 25(3), pages 597-614, July.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:3:d:10.1007_s00780-021-00459-2
    DOI: 10.1007/s00780-021-00459-2
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    References listed on IDEAS

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    Cited by:

    1. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, December.
    2. Yi Shen & Zachary Van Oosten & Ruodu Wang, 2024. "Partial Law Invariance and Risk Measures," Papers 2401.17265, arXiv.org, revised Jun 2024.
    3. Zang, Xin & Jiang, Fan & Xia, Chenxi & Yang, Jingping, 2024. "Random distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 51-73.
    4. Ruodu Wang & Zhenyuan Zhang, 2022. "Simultaneous Optimal Transport," Papers 2201.03483, arXiv.org, revised May 2023.
    5. Mononen, Lasse, 2024. "Dynamically Consistent Intertemporal Dual-Self Expected Utility," Center for Mathematical Economics Working Papers 686, Center for Mathematical Economics, Bielefeld University.

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    More about this item

    Keywords

    Time-consistency; Commonotonicity; Atomless probability spaces;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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