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Conditional Risk Mappings

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Author Info

  • Andrzej Ruszczynski

    (Rutgers University)

  • Alexander Shapiro

    (Georgia Institute of Technology)

Abstract

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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Bibliographic Info

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
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Web page: http://128.118.178.162

Related research

Keywords: Risk; Convex Analysis; Conjugate Duality; Stochastic Optimization; Dynamic Programming; Multi-Stage Programming;

This paper has been announced in the following NEP Reports:

References

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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. 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.
  3. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, EconWPA, revised 08 Oct 2005.
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Citations

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Cited by:
  1. Stadje, Mitja, 2010. "Extending dynamic convex risk measures from discrete time to continuous time: A convergence approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 391-404, December.
  2. Jing Li & Mingxin Xu, 2013. "Optimal Dynamic Portfolio with Mean-CVaR Criterion," Risks, MDPI, Open Access Journal, vol. 1(3), pages 119-147, November.
  3. Pelsser, A. & Stadje, M.A., 2012. "Time-Consistent and Market-Consistent Evaluations (Revised version of CentER DP 2011-063)," Discussion Paper 2012-086, Tilburg University, Center for Economic Research.
  4. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
  5. Zachary Feinstein & Birgit Rudloff, 2012. "Multi-portfolio time consistency for set-valued convex and coherent risk measures," Papers 1212.5563, arXiv.org, revised May 2014.
  6. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Oct 2013.
  7. Shapiro, Alexander, 2012. "Minimax and risk averse multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 219(3), pages 719-726.
  8. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
  9. Li, Jing & Xu, Mingxin, 2009. "Minimizing Conditional Value-at-Risk under Constraint on Expected Value," MPRA Paper 26342, University Library of Munich, Germany, revised 25 Oct 2010.
  10. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, EconWPA.

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