Journal of Mathematical Sciences

, Volume 133, Issue 4, pp 1422–1444 | Cite as

Sequential Importance Sampling Algorithms for Dynamic Stochastic Programming

  • M. A. H. Dempster


This paper gives a comprehensive treatment of EVPI-based sequential importance sampling algorithms for dynamic (multistage) stochastic programming problems. Both theory and computational algorithms are discussed. Under general assumptions it is shown that both an expected value of perfect information (EVPI) process and the corresponding marginal EVPI process (the supremum norm of the conditional expectation of its generalized derivative) are nonanticipative nonnegative supermartingales. These processes are used as importance criteria in the class of sampling algorithms treated in the paper. When their values are negligible at a node of the current sample problem scenario tree, scenarios descending from the node are replaced by a single scenario at the next iteration. On the other hand, high values lead to increasing the number of scenarios descending from the node. Both the small sample and asymptotic properties of the sample problem estimates arising from the algorithms are established, and the former are evaluated numerically in the context of a financial planning problem. Finally, current and future research is described. Bibliography: 49 titles.


Planning Problem Asymptotic Property Conditional Expectation Stochastic Program Computational Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • M. A. H. Dempster
    • 1
    • 2
  1. 1.Centre for Financial Research, Judge Institute of Management StudiesUniversity of CambridgeCambridgeUK
  2. 2.Cambridge Systems Associates LimitedCambridgeUK

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