Mathematical Programming

, Volume 153, Issue 2, pp 459–493 | Cite as

Time-consistent approximations of risk-averse multistage stochastic optimization problems

  • Tsvetan Asamov
  • Andrzej Ruszczyński
Full Length Paper Series A


In this paper we study the concept of time consistency as it relates to multistage risk-averse stochastic optimization problems on finite scenario trees. We use dynamic time-consistent formulations to approximate problems having a single coherent risk measure applied to the aggregated costs over all time periods. The dual representation of coherent risk measures is used to create a time-consistent cutting plane algorithm. Additionally, we also develop methods for the construction of universal time-consistent upper bounds, when the objective function is the mean-semideviation measure of risk. Our numerical results indicate that the resulting dynamic formulations yield close approximations to the original problem.


Dynamic measures of risk Time consistency Decomposition 

Mathematics Subject Classification

90C15 90C25 49M27 


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  1. 1.Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Department of Management Science and Information SystemsRutgers UniversityPiscatawayUSA

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