Minimax and risk averse multistage stochastic programming

► We study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. ► We discuss conditions for time consistency of such formulations of stochastic problems. ► We also describe a connection between law invariant coherent risk measures and the...

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Bibliographic Details
Published in:European journal of operational research Vol. 219; no. 3; pp. 719 - 726
Main Author: Shapiro, Alexander
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.06.2012
Elsevier
Elsevier Sequoia S.A
Subjects:
Applied sciences
Coherent risk measures
Dynamic equations
Exact sciences and technology
Inventory control, production control. Distribution
Inventory management
Mathematical programming
Operational research and scientific management
Operational research. Management science
Problem of moments
Reliability theory. Replacement problems
Risk assessment
Risk averse stochastic optimization
Risk aversion
Risk theory. Actuarial science
Robust optimization
Stochastic models
Stochastic programming
Studies
Dynamic equations
Coherent risk measures
Robust optimization
Problem of moments
Risk averse stochastic optimization
Stochastic programming
Modeling
Risk aversion
Uncertain system
Invariant measure
Minimax problem
Minimax method
Inventory control
Moment problem
Robustness
Temporal coherence
Risk management
Probability measure
Mathematical programming
ISSN:0377-2217, 1872-6860
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Summary:► We study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. ► We discuss conditions for time consistency of such formulations of stochastic problems. ► We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. Finally, we discuss a minimax approach with moment constraints to the classical inventory model.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2011.11.005