2006-12-14Buch DOI: 10.18452/2994
Stability of multistage stochastic programs incorporating polyhedral risk measures
We analyse stability aspects of linear multistage stochastic programs with polyhedral risk measures in the objective. In particular, we consider sensitivity of the optimal value with respect perturbations of the underlying stochastic input process. An existing stability result for multistage stochastic programs with 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 stochastic process. We discuss additional requirements for the polyhedral risk measures such that the problem dependent ﬁltration distances can be bounded by problem independent ones. Stability and such bounds are the basis for scenario tree approximation techniques used in practical problem solving.
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