Annals of Operations Research

, Volume 152, Issue 1, pp 5–22 | Cite as

Coherent multiperiod risk adjusted values and Bellman’s principle

  • Philippe ArtznerEmail author
  • Freddy Delbaen
  • Jean-Marc Eber
  • David Heath
  • Hyejin Ku


Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as in decision-making. We finally deduce risk measurements for the final value of locked-in positions and repeat a warning concerning Tail-Value-at-Risk.


Bellman’s principle Capital requirement Coherence Risk-adjusted values Stability by pasting Time consistency 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Philippe Artzner
    • 1
    Email author
  • Freddy Delbaen
    • 2
  • Jean-Marc Eber
    • 3
  • David Heath
    • 4
  • Hyejin Ku
    • 5
  1. 1.Institut de Recherche Mathématique AvancéeStrasbourgFrance
  2. 2.Eidgenössische Technische HochschuleZurichSwitzerland
  3. 3.LexifiParisFrance
  4. 4.Carnegie Mellon UniversityPittsburghUSA
  5. 5.York UniversityNew YorkUSA

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