Risk measures with the CxLS property View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-10-01

AUTHORS

Freddy Delbaen, Fabio Bellini, Valeria Bignozzi, Johanna F. Ziegel

ABSTRACT

In the present contribution, we characterise law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (Math. Finance 16:419–441, 2006), we show that these risk measures can be identified with a class of generalised shortfall risk measures. As a direct consequence, we are able to extend the results in Ziegel (Math. Finance, 2014, http://onlinelibrary.wiley.com/doi/10.1111/mafi.12080/abstract) and Bellini and Bignozzi (Quant. Finance 15:725–733, 2014) on convex elicitable risk measures and confirm that expectiles are the only elicitable coherent risk measures. Further, we provide a simple characterisation of robustness for convex risk measures in terms of a weak notion of mixture continuity. More... »

PAGES

433-453

References to SciGraph publications

  • 2002-10. Convex measures of risk and trading constraints in FINANCE AND STOCHASTICS
  • 2008-07-29. Dual characterization of properties of risk measures on Orlicz hearts in MATHEMATICS AND FINANCIAL ECONOMICS
  • 2001. On law invariant coherent risk measures in ADVANCES IN MATHEMATICAL ECONOMICS
  • 2006. Law invariant risk measures have the Fatou property in ADVANCES IN MATHEMATICAL ECONOMICS
  • 2005. Law invariant convex risk measures in ADVANCES IN MATHEMATICAL ECONOMICS
  • 2007-02-08. Dilatation monotone risk measures are law invariant in FINANCE AND STOCHASTICS
  • 2014-01-16. Comparative and qualitative robustness for law-invariant risk measures in FINANCE AND STOCHASTICS
  • 1989-12. Axiomatic utility theories with the betweenness property in ANNALS OF OPERATIONS RESEARCH
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00780-015-0279-6

    DOI

    http://dx.doi.org/10.1007/s00780-015-0279-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1016111594


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