The strictest common relaxation of a family of risk measures
AbstractOperations which form new risk measures from a collection of given (often simpler) risk measures have been used extensively in the literature. Examples include convex combination, convolution, and the worst-case operator. Here we study the risk measure that is constructed from a family of given risk measures by the best-case operator; that is, the newly constructed risk measure is defined as the one that is as restrictive as possible under the condition that it accepts all positions that are accepted under any of the risk measures from the family. In fact we define this operation for conditional risk measures, to allow a multiperiod setting. We show that the well-known VaR risk measure can be constructed from a family of conditional expectations by a combination that involves both worst-case and best-case operations. We provide an explicit description of the acceptance set of the conditional risk measure that is obtained as the strictest common relaxation of two given conditional risk measures.
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Bibliographic InfoPaper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-5241367.
Date of creation: 2011
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Publication status: Published in Insurance : Mathematics & Economics (2011) v.48, p.29-34
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Other versions of this item:
- Roorda, Berend & Schumacher, J.M., 2011. "The strictest common relaxation of a family of risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 29-34, January.
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