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A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective

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  • Tomasz R. Bielecki
  • Igor Cialenco
  • Marcin Pitera

Abstract

In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout are the notion of the LM-measure and the notion of the update rule that, we believe, are the key tools for studying time consistency in a unified framework.

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  • Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2016. "A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective," Papers 1603.09030, arXiv.org, revised Jan 2017.
    • Handle: RePEc:arx:papers:1603.09030
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Cosimo Munari & Lutz Wilhelmy & Stefan Weber, 2021. "Capital Requirements and Claims Recovery: A New Perspective on Solvency Regulation," Papers 2107.10635, arXiv.org.
    2. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2018. "A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 204-221, February.
    3. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2019. "Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion," Papers 1904.01745, arXiv.org.
    4. Haodong Yu & Jie Sun & Yanjun Wang, 2021. "A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure," Computational Optimization and Applications, Springer, vol. 79(1), pages 67-99, May.
    5. Christos E. Kountzakis & Damiano Rossello, 2019. "Acceptability Indices of Performance for Bounded C\`adl\`ag Processes," Papers 1911.02261, arXiv.org.
    6. Marlon Moresco & M'elina Mailhot & Silvana M. Pesenti, 2023. "Uncertainty Propagation and Dynamic Robust Risk Measures," Papers 2308.12856, arXiv.org, revised Feb 2024.
    7. Ziteng Cheng & Sebastian Jaimungal, 2022. "Risk-Averse Markov Decision Processes through a Distributional Lens," Papers 2203.09612, arXiv.org, revised Apr 2024.
    8. E. Kromer & L. Overbeck & K. Zilch, 2019. "Dynamic systemic risk measures for bounded discrete time processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 77-108, August.
    9. Jin Ma & Ting-Kam Leonard Wong & Jianfeng Zhang, 2018. "Time-consistent conditional expectation under probability distortion," Papers 1809.08262, arXiv.org, revised Jun 2020.
    10. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2019. "Time-consistency of risk measures: how strong is such a property?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 287-317, June.
    11. Shapiro, Alexander, 2021. "Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 288(1), pages 1-13.
    12. Tomasz R. Bielecki & Igor Cialenco & Shibi Feng, 2018. "A Dynamic Model of Central Counterparty Risk," Papers 1803.02012, arXiv.org.
    13. Saul Jacka & Seb Armstrong & Abdel Berkaoui, 2017. "Multi-currency reserving for coherent risk measures," Papers 1712.01319, arXiv.org, revised Dec 2017.
    14. Cosimo Munari & Stefan Weber & Lutz Wilhelmy, 2023. "Capital requirements and claims recovery: A new perspective on solvency regulation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 329-380, June.
    15. Tomasz R. Bielecki & Tao Chen & Igor Cialenco, 2020. "Time-inconsistent Markovian control problems under model uncertainty with application to the mean-variance portfolio selection," Papers 2002.02604, arXiv.org, revised Sep 2020.
    16. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2021. "Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 683-721, April.
    17. Tomasz R. Bielecki & Igor Cialenco & Shibi Feng, 2018. "A Dynamic Model Of Central Counterparty Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-34, December.
    18. Strub, Moris S. & Li, Duan & Cui, Xiangyu & Gao, Jianjun, 2019. "Discrete-time mean-CVaR portfolio selection and time-consistency induced term structure of the CVaR," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).

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