Finance and Stochastics

, Volume 9, Issue 4, pp 539–561

Conditional and dynamic convex risk measures



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. A suitable 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. As a reference example, illustrating all the proposed developments, we introduce a suitably defined dynamic version of the class of entropic risk measures.


Conditional convex risk measure robust representation entropic risk measure dynamic convex risk measure time-consistency 


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Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Center for Applied Statistics and EconomicsHumboldt Universität BerlinBerlinGermany
  2. 2.Dipartimento di Matematica per le DecisioniUniversitá di FirenzeFirenzeItaly

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