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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| Vydané v: | European journal of operational research Ročník 219; číslo 3; s. 719 - 726 |
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| Jazyk: | English |
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Amsterdam
Elsevier B.V
16.06.2012
Elsevier Elsevier Sequoia S.A |
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | ► 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. |
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| AbstractList | 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. [PUBLICATION ABSTRACT] ► 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. |
| Author | Shapiro, Alexander |
| Author_xml | – sequence: 1 givenname: Alexander surname: Shapiro fullname: Shapiro, Alexander email: ashapiro@isye.gatech.edu organization: School of Industrial & Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332, United States |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Minimax and risk averse multistage stochastic programming |
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