2006-12-14Buch DOI: 10.18452/8369
Stability of multistage stochastic programs incorporating polyhedral risk measures
We analyse stability aspects of linear multistage stochastic programs with polyhedral risk measures inthe objective. In particular, we consider sensitivity of the optimal value with respect perturbations ofthe underlying stochastic input process. An existing stability result for multistage stochastic programswith expectation objective is carried forward to the case of polyhedral risk-averse objectives. Beside$L_r$-distances these results also involve ﬁltration distances of the perturbations of the stochasticprocess. We discuss additional requirements for the polyhedral risk measures such that the problemdependent ﬁltration distances can be bounded by problem independent ones. Stability and suchbounds are the basis for scenario tree approximation techniques used in practical problem solving.
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