Conditional risk mappings

Andrzej Ruszczyński, Alexander Shapiro

Research output: Contribution to journalArticlepeer-review

127 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)544-561
Number of pages18
JournalMathematics of Operations Research
Issue number3
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research


  • Conjugate duality
  • Dynamic programming
  • Multistage stochastic programming
  • Risk
  • Stochastic optimization


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