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On s-additive robust representation of convex risk measures for unbounded financial positions in the presence of uncertainty about the market model

By Volker Krätschmer

Abstract

Recently, Frittelli and Scandolo ([9]) extend the notion of risk measures, originally introduced by Artzner, Delbaen, Eber and Heath ([1]), to the risk assessment of abstract financial positions, including pay offs spread over different dates, where liquid derivatives are admitted to serve as financial instruments. The paper deals with s-additive robust representations of convex risk measures in the extended sense, dropping the assumption of an existing market model, and allowing also unbounded financial positions. The results may be applied for the case that a market model is available, and they encompass as well as improve criteria obtained for robust representations of the original convex risk measures for bounded positions ([4], [7], [16]).Convex risk measures, model uncertainty, s-additive robust representation, Fatou property, nonsequential Fatou property, strong s-additive robust representation, Krein-Smulian theorem, Greco theorem, inner Daniell stone theorem, general Dini theorem, Simons’ lemma.

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Citations

  1. (1972). A convergence theorem with boundary,
  2. (1987). Angelic spaces and the double limit relation,
  3. (1984). Applied Nonlinear Analysis”,
  4. atschmer, Compactness in spaces of inner regular measures and a general Portmanteau lemma, SFB 649 discussion paper 2006-081, downloadable at http://sfb649.wiwi.hu-berlin.de.
  5. (2005). atschmer, Robust representation of convex risk measures by probability measure,
  6. (2002). Coherent Measures of Risk on General Probability Spaces, in:
  7. (1999). Coherent measures of risk,
  8. (1977). Convex Analysis and Measurable Multifunctions”,
  9. (2006). Distribution-invariant dynamic risk measures, information, and dynamic consistency,
  10. (2004). Dynamic Coherent Risk Measures,
  11. (2004). Dynamic Convex Risk Measures,
  12. (2006). Law invariant risk measures have the Fatou property,
  13. (1994). Non-Additive Measure and Integral”,
  14. (1997). On some basic theorems in convex analysis,
  15. (1998). onig, Measure and Integration: Integral representations of isotone functionals,
  16. (2006). Optimization of convex risk functions,
  17. (1978). Probabilities and Potential”, North-Holland,
  18. (2006). Risk measures and capital requirements for processes,