Complexity of Bilevel Coherent Risk Programming
نویسنده
چکیده
This paper considers a bilevel programming approach to applying coherent risk measures to extended two-stage stochastic programming problems. This formulation technique avoids the time-inconsistency issues plaguing naive models and the incomposability issues which cause time-consistent formulations to have complicated, hard-to-explain objective functions. Unfortunately, the analysis here shows that such bilevel formulations, when using the standard mean-semideviation and average-value-at-risk measures, are NP-hard. While not necessarily indicating that solution of such models is impractical, these results suggest that it may prove difficult and will likely require some kind of implicit enumeration method. Acknowledgements: This work was supported by a grant from the Air Force Office of Scientific Research, award FA9550-11-1-0164. The author would like to thank Andrzej Ruszczyński for his assistance.
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تاریخ انتشار 2012