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 dicult and will likely require some kind of implicit enumeration method.

## Citation

RUTCOR Research Report 17-2012, Rutgers University, April 2012