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


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.

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Corresponding author

Correspondence to Andrzej Ruszczyński.

Additional information

This work was supported by the Air Force Office of Scientific Research (award FA9550-11-1-0164), and by the National Science Foundation (award DMS-1312016).

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Asamov, T., Ruszczyński, A. Time-consistent approximations of risk-averse multistage stochastic optimization problems. Math. Program. 153, 459–493 (2015).

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  • Dynamic measures of risk
  • Time consistency
  • Decomposition

Mathematics Subject Classification

  • 90C15
  • 90C25
  • 49M27