Mathematical Programming

, Volume 152, Issue 1–2, pp 275–300

Evaluating policies in risk-averse multi-stage stochastic programming

Full Length Paper Series A


We consider a risk-averse multi-stage stochastic program using conditional value at risk as the risk measure. The underlying random process is assumed to be stage-wise independent, and a stochastic dual dynamic programming (SDDP) algorithm is applied. We discuss the poor performance of the standard upper bound estimator in the risk-averse setting and propose a new approach based on importance sampling, which yields improved upper bound estimators. Modest additional computational effort is required to use our new estimators. Our procedures allow for significant improvement in terms of controlling solution quality in SDDP-style algorithms in the risk-averse setting. We give computational results for multi-stage asset allocation using a log-normal distribution for the asset returns.


Multi-stage stochastic programming Stochastic dual dynamic programming Importance sampling Risk-averse optimization 

Mathematics Subject Classification (2010)

90C15 49M27 

Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  1. 1.Department of Probability and Mathematical StatisticsCharles University in Prague, Faculty of Mathematics and PhysicsPragueCzech Republic
  2. 2.Graduate Program in Operations Research and Industrial EngineeringThe University of Texas at AustinAustinUSA

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