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Dynamic quasi concave performance measures

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  • Biagini, Sara
  • Bion-Nadal, Jocelyne

Abstract

We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characterization of a CPM in terms of an induced family of conditional convex risk measures. In the case of indexes these risk measures are coherent. Then, Dynamic Performance Measures (DPMs) are introduced and the problem of time consistency is addressed. The definition of time consistency chosen here ensures that the positions which are considered good tomorrow are already considered good today. Finally, we investigate the relation between time consistency for a DPM and weak acceptance consistency for the induced families of risk measures.

Suggested Citation

  • Biagini, Sara & Bion-Nadal, Jocelyne, 2014. "Dynamic quasi concave performance measures," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 143-153.
    • Handle: RePEc:eee:mateco:v:55:y:2014:i:c:p:143-153
    DOI: 10.1016/j.jmateco.2014.02.007
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    References listed on IDEAS

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    Citations

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    Cited by:

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    2. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2014. "A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time," Papers 1409.7028, arXiv.org, revised Sep 2017.
    3. Sigrid Källblad, 2017. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Finance and Stochastics, Springer, vol. 21(2), pages 397-425, April.
    4. Tomasz R. Bielecki & Igor Cialenco & Tao Chen, 2014. "Dynamic Conic Finance via Backward Stochastic Difference Equations," Papers 1412.6459, arXiv.org, revised Dec 2014.
    5. Tomasz R. Bielecki & Igor Cialenco & Hao Liu, 2023. "Time consistency of dynamic risk measures and dynamic performance measures generated by distortion functions," Papers 2309.02570, arXiv.org, revised Sep 2023.
    6. 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.
    7. Righi, Marcelo Brutti, 2024. "Star-shaped acceptability indexes," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 170-181.
    8. 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.
    9. 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.

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