Conditional Risk Mappings

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Conditional Risk Mappings

Author Info

Andrzej Ruszczynski (Rutgers University)
Alexander Shapiro (Georgia Institute of Technology)

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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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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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This paper has been announced in the following NEP Reports:

NEP-ALL-2004-04-18 (All new papers)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, EconWPA, revised 08 Oct 2005. [Downloadable!]
Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July. [Downloadable!] (restricted)
Other versions:
- 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. [Downloadable!]
Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447. [Downloadable!] (restricted)
Other versions:
- H. Föllmer & A. Schied, . "Convex measures of risk and trading constraints," Sonderforschungsbereich 373 2001-71, Humboldt Universitaet Berlin.

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Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, EconWPA. [Downloadable!]

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