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Dynamic Risk Measures

In: Advanced Mathematical Methods for Finance

Author

Listed:
  • Beatrice Acciaio

    (University of Perugia, Department of Economy, Finance and Statistics)

  • Irina Penner

    (Humboldt-Universität zu Berlin, Institut für Mathematik)

Abstract

This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete-time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time consistency properties of dynamic risk measures in terms of acceptance sets, penalty functions, and by supermartingale properties of risk processes and penalty functions.

Suggested Citation

  • Beatrice Acciaio & Irina Penner, 2011. "Dynamic Risk Measures," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 1-34, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18412-3_1
    DOI: 10.1007/978-3-642-18412-3_1
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    Citations

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    Cited by:

    1. Anthony Coache & Sebastian Jaimungal, 2021. "Reinforcement Learning with Dynamic Convex Risk Measures," Papers 2112.13414, arXiv.org, revised Nov 2022.
    2. Belhouari, Oussama & Devolder, Pierre & Linders, Daniel, 2025. "The Three-step method in a dynamic setting," LIDAM Discussion Papers ISBA 2025018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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