Sampling-Based Decomposition Methods for Multistage Stochastic Programs Based on Extended Polyhedral Risk Measures

2012 ◽  
Vol 22 (2) ◽  
pp. 286-312 ◽  
Author(s):  
Vincent Guigues ◽  
Werner Römisch
Keyword(s):  
Risk Measures ◽  
Decomposition Methods ◽  
Stochastic Programs ◽  
Multistage Stochastic Programs

scholarly journals On Solving Multistage Stochastic Programs with Coherent Risk Measures

2013 ◽  
Vol 61 (4) ◽  
pp. 957-970 ◽  
Author(s):  
Andy Philpott ◽  
Vitor de Matos ◽  
Erlon Finardi
Keyword(s):  
Risk Measures ◽  
Coherent Risk Measures ◽  
Stochastic Programs ◽  
Coherent Risk ◽  
Multistage Stochastic Programs

Consistency of Sample Estimates of Risk Averse Stochastic Programs

2013 ◽  
Vol 50 (02) ◽  
pp. 533-541 ◽  
Author(s):  
Alexander Shapiro
Keyword(s):  
Stochastic Programming ◽  
Law Of Large Numbers ◽  
Risk Measures ◽  
Regularity Conditions ◽  
Distributed Data ◽  
Risk Averse ◽  
Asymptotic Consistency ◽  
Stochastic Programs ◽  
Large Numbers ◽  
Independent Identically Distributed

In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent, identically distributed data. Under mild regularity conditions, we prove a law of large numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems.

A Scalable Bounding Method for Multistage Stochastic Programs

2017 ◽  
Vol 27 (3) ◽  
pp. 1772-1800 ◽  
Author(s):  
Burhaneddi̇n Sandikçi ◽  
Osman Y. Özaltin
Keyword(s):  
Stochastic Programs ◽  
Multistage Stochastic Programs

Periodical Multistage Stochastic Programs

2020 ◽  
Vol 30 (3) ◽  
pp. 2083-2102
Author(s):  
Alexander Shapiro ◽  
Lingquan Ding
Keyword(s):  
Stochastic Programs ◽  
Multistage Stochastic Programs
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