Publikation:

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

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2011

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Cheridito, Patrick

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https://doi.org/10.1142/S0219024911006292
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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.

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Fachgebiet (DDC)
510 Mathematik

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Dynamic risk measures, time-consistency, dual representations

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ISO 690CHERIDITO, 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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