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Conditional and dynamic convex risk measures

Kai Detlefsen (detlefsen@wiwi.hu-berlin.de) and Giacomo Scandolo (giacomo.scandolo@unifi.it)

Finance and Stochastics, 2005, vol. 9, issue 4, 539-561

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. 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. Copyright Springer-Verlag Berlin/Heidelberg 2005

Keywords: Conditional convex risk measure; robust representation; entropic risk measure; dynamic convex risk measure; time-consistency (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (170)

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DOI: 10.1007/s00780-005-0159-6

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