Composition of Time-Consistent Dynamic Monetary Risk Measures in Discrete Time

Cheridito, Patrick; Kupper, Michael

Composition of Time-Consistent Dynamic Monetary Risk Measures in Discrete Time

Dateien

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Datum

2011

Autor:innen

Cheridito, Patrick

Kupper, Michael

DOI (zitierfähiger Link)

https://doi.org/10.1142/S0219024911006292

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

International Journal of Theoretical and Applied Finance. World Scientific Publishing. 2011, 14(1), pp. 137-162. ISSN 0219-0249. eISSN 1793-6322. Available under: doi: 10.1142/S0219024911006292

Zusammenfassung

In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for time-consistent convex monetary risk measures in terms of one-step penalty functions. We first study risk measures for random variables modelling financial positions at a fixed future time. Then we consider the more general case of risk measures that depend on stochastic processes describing the evolution of financial positions or cumulated cash flows. In both cases the new representations allow for a simple composition of one-step risk measures in the dual. We discuss several explicit examples and provide connections to the recently introduced class of dynamic variational preferences.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Dynamic risk measures, time-consistency, dual representations

Zitieren

ISO 690

CHERIDITO, Patrick, Michael KUPPER, 2011. Composition of Time-Consistent Dynamic Monetary Risk Measures in Discrete Time. In: International Journal of Theoretical and Applied Finance. World Scientific Publishing. 2011, 14(1), pp. 137-162. ISSN 0219-0249. eISSN 1793-6322. Available under: doi: 10.1142/S0219024911006292

BibTex

@article{Cheridito2011Compo-55459,
  year={2011},
  doi={10.1142/S0219024911006292},
  title={Composition of Time-Consistent Dynamic Monetary Risk Measures in Discrete Time},
  number={1},
  volume={14},
  issn={0219-0249},
  journal={International Journal of Theoretical and Applied Finance},
  pages={137--162},
  author={Cheridito, Patrick and Kupper, Michael}
}

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