2011-11-28Buch DOI: 10.18452/3044
Pflug, Georg Ch.
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
We provide a new identity for the multistage Average Value-at-Risk. The identity is based on the conditional Average Value-at-Risk at random level, which is introduced. It is of interest in situations, where the information available increases over time, so it is – among other applications – customized to multistage optimization. The identity relates to dynamic programming and is adapted to problems which involve the Average Value-at-Risk in its objective. We elaborate further dynamic programming equations for speciﬁc multistage optimization problems and derive a characterizing martingale property for the value function. The concept solves a particular aspect of time consistency and is adapted for situations, where decisions are planned and executed consecutively in subsequent instants of time. We discuss the approach for other risk measures, which are in frequent use for decision making under uncertainty, particularly for ﬁnancial decisions.
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