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Conditional and dynamic convex risk measures

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  • Detlefsen, Kai
  • Scandolo, Giacomo

Abstract

We extend the definition of a convex risk measure to a conditional framework where additional information is available. We characterize these risk measures through the associated acceptance sets and prove a representation result in terms of conditional expectations. As an example we consider the class of conditional entropic risk measures. A new regularity property of conditional risk measures is defined and discussed. Finally we introduce the concept of a dynamic convex risk measure as a family of successive conditional convex risk measures and characterize those satisfying some natural time consistency properties.

Suggested Citation

  • Detlefsen, Kai & Scandolo, Giacomo, 2005. "Conditional and dynamic convex risk measures," SFB 649 Discussion Papers 2005-006, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2005-006
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    References listed on IDEAS

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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    4. Weber, Stefan, 2003. "Distribution-Invariant Dynamic Risk Measures," SFB 373 Discussion Papers 2003,53, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2024. "Dynamic capital allocation rules via BSDEs: an axiomatic approach," Annals of Operations Research, Springer, vol. 336(1), pages 749-772, May.
    2. Oscar Dowson & David P. Morton & Bernardo K. Pagnoncelli, 2025. "Incorporating convex risk measures into multistage stochastic programming algorithms," Annals of Operations Research, Springer, vol. 348(2), pages 807-831, May.
    3. Arthur Charpentier, 2018. "An introduction to multivariate and dynamic risk measures," Working Papers hal-01831481, HAL.

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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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