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

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• 作者：Tsvetan Asamov ; Andrzej Ruszczyński
• 关键词：Dynamic measures of risk ; Time consistency ; Decomposition ; 90C15 ; 90C25 ; 49M27
• 刊名：Mathematical Programming
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：153
• 期：2
• 页码：459-493
• 全文大小：2,231 KB
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• 作者单位：Tsvetan Asamov (1)
  Andrzej Ruszczyński (2)
  
  1. Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, 08544, USA
  2. Department of Management Science and Information Systems, Rutgers University, 94 Rockefeller Road, Piscataway, NJ, 08854, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Mathematics of Computing
  Numerical Analysis
  Combinatorics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-4646

文摘

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. Keywords Dynamic measures of risk Time consistency Decomposition