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Mathematical Programming

, Volume 152, Issue 1–2, pp 275–300 | Cite as

Evaluating policies in risk-averse multi-stage stochastic programming

  • Václav Kozmík
  • David P. Morton
Full Length Paper Series A

Abstract

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.

Keywords

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

Mathematics Subject Classification (2010)

90C15 49M27 

Notes

Acknowledgments

We thank two anonymous referees and an Associate Editor for comments that improved the paper. The research was partly supported by the Czech Science Foundation through grant 402/12/G097, by the Defense Threat Reduction Agency through Grant HDTRA1-08-1-0029, and by the National Science Foundation through Grant ECCS-1162328.

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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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