|edoc-Server der Humboldt-Universität zu Berlin|
Georg Ch. Pflug, University of Vienna|
Alois Pichler, University of Vienna
|Date of Acceptance:||28.11.2011|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
|Complete Preprint:||pdf (urn:nbn:de:kobv:11-100196802)|
|Keywords (eng):||time consistency, risk measure, dynamic programming, stochastic optimization, Average Value-at-Risk|
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|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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