Conditional Risk Mappings

Andrzej Ruszczynski; Alexander Shapiro

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SPEPS Preprint

Author(s):	Andrzej Ruszczynski, Rutgers University Alexander Shapiro, Georgia Institute of Technology
Title:	Conditional Risk Mappings
Date of Acceptance:	25.03.2004
Submission Date:	09.03.2004
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10059486)
Keywords (eng):	Risk, Convex Analysis, Conjugate Duality, Stochastic Optimization, Dynamic Programming, Multi-stage Programming
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Abstract (eng):

We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. 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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