期刊
SIAM JOURNAL ON FINANCIAL MATHEMATICS
卷 1, 期 1, 页码 66-95出版社
SIAM PUBLICATIONS
DOI: 10.1137/080743494
关键词
set-valued risk measures; coherent risk measures; Legendre-Fenchel transform; convex duality; biconjugation; value at risk; scalarization
Extending the approach of Jouini, Meddeb, and Touzi [Finance Stoch., 8 (2004), pp. 531-552] we define set-valued (convex) measures of risk and their acceptance sets, and we give dual representation theorems. A scalarization concept is introduced that has a meaning in terms of internal prices of portfolios of reference instruments. Using primal and dual descriptions, we introduce new examples for set-valued measures of risk, e. g., set-valued upper expectations, value at risk, average value at risk, and entropic risk measure.
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