Algorithmic Aspects of Scenario-Based Multi-stage Decision Process Optimization
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
A multiobjective metaheuristic for a mean-risk multistage capacity investment problem
Journal of Heuristics
A multiobjective metaheuristic for a mean-risk static stochastic knapsack problem
Computational Optimization and Applications
Risk Averse Shape Optimization
SIAM Journal on Control and Optimization
Evolutionary multi-stage financial scenario tree generation
EvoCOMNET'10 Proceedings of the 2010 international conference on Applications of Evolutionary Computation - Volume Part II
On a time consistency concept in risk averse multistage stochastic programming
Operations Research Letters
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We consider stochastic programs with risk measures in the objective and study stability properties as well as decomposition structures. Thereby we place emphasis on dynamic models, i.e., multistage stochastic programs with multiperiod risk measures. In this context, we define the class of polyhedral risk measures such that stochastic programs with risk measures taken from this class have favorable properties. Polyhedral risk measures are defined as optimal values of certain linear stochastic programs where the arguments of the risk measure appear on the right-hand side of the dynamic constraints. Dual representations for polyhedral risk measures are derived and used to deduce criteria for convexity and coherence. As examples of polyhedral risk measures we propose multiperiod extensions of the Conditional-Value-at-Risk.