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Conditional Risk Mappings

  • Andrzej Ruszczynski

    (Rutgers University)

  • Alexander Shapiro

    (Georgia Institute of Technology)

We introduce an axiomatic definition of a conditional convex risk mapping. By employing the techniques of conjugate duality we derive properties of conditional risk mappings. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings.

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File URL: http://128.118.178.162/eps/ri/papers/0404/0404002.pdf
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Paper provided by EconWPA in its series Risk and Insurance with number 0404002.

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Length: 21 pages
Date of creation: 12 Apr 2004
Date of revision: 08 Oct 2005
Handle: RePEc:wpa:wuwpri:0404002
Note: Type of Document - pdf; pages: 21
Contact details of provider: Web page: http://128.118.178.162

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  1. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
  2. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, EconWPA, revised 08 Oct 2005.
  3. W. Ogryczak & A. Ruszczynski, 1997. "From Stochastic Dominance to Mean-Risk Models: Semideviations as Risk Measures," Working Papers ir97027, International Institute for Applied Systems Analysis.
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