Measuring risk with multiple eligible assets

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• 作者：Walter Farkas (1)
  Pablo Koch-Medina (2)
  Cosimo Munari (3)
  
  1. Department of Banking and Finance ; University of Zurich and ETH Zurich ; Plattenstrasse 14 ; 8032 ; 聽Zurich ; Switzerland
  2. Department of Banking and Finance ; University of Zurich ; Plattenstrasse 14 ; 8032 ; 聽Zurich ; Switzerland
  3. Department of Mathematics ; ETH Zurich ; R盲mistrasse 101 ; 8092 ; 聽Zurich ; Switzerland
  
• 关键词：Risk measures ; Multiple eligible assets ; Acceptance sets ; Dual representations ; Set ; valued risk measures ; 91B30 ; 46A40 ; 46A20 ; 46A22
• 刊名：Mathematics and Financial Economics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：9
• 期：1
• 页码：3-27
• 全文大小：321 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Quantitative Finance
  Finance and Banking
  Financial Economics
  Game Theory and Mathematical Methods
  Applications of Mathematics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1862-9660

文摘

The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and continuity properties of these risk measures with respect to multiple eligible assets. Our finiteness and continuity results highlight the interplay between the acceptance set and the class of eligible portfolios. We present a simple, alternative approach to the dual representation of convex risk measures by directly applying to the acceptance set the external characterization of closed, convex sets. We prove that risk measures are nondegenerate if and only if the pricing functional admits a positive extension which is a supporting functional for the underlying acceptance set, and provide a characterization of when such extensions exist. Finally, we discuss applications to set-valued risk measures, superhedging with shortfall risk, and optimal risk sharing.