We consider stochastic programs with risk measures in the objective and study stability properties as well as decomposition structures. Thereby we place emphasis on dynamic models, i.e., multistage stochastic programs with multiperiod risk measures. In this context, we define the class of polyhedral risk measures such that stochastic programs with risk measures taken from this class have favorable properties. Polyhedral risk measures are defined as optimal values of certain linear stochastic programs where the arguments of the risk measure appear on the right-hand side of the dynamic constraints. Dual representations for polyhedral risk measures are derived and used to deduce criteria for convexity and coherence. As examples of polyhedral risk measures we propose multiperiod extensions of the Conditional-Value-at-Risk.

؉ and CD8 ؉ T cells was observed upon stimulation with miltefosine-treated, infected DC. In addition, miltefosine application in vivo did not lead to maturation/emigration of skin DC. DC NO ؊ production, a mechanism used by phagocytes to rid themselves of intracellular parasites, was also unaltered upon miltefosine treatment. Our data confirm prior studies indicating that in contrast to, e.g., pentavalent antimonials, miltefosine functions independently of the immune system, mostly through direct toxicity against the Leishmania parasite.

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We consider empirical approximations (sample average approximations) of two-stage stochastic mixed-integer linear programs and derive central limit theorems for the objectives and optimal values. The limit theorems are based on empirical process theory and the functional delta method. We also show how these limit theorems can be used to derive confidence intervals for optimal values via resampling methods (bootstrap, subsampling).

Abstract-The possibility of controlling risk in stochastic power optimization by incorporating special risk functionals, socalled polyhedral risk measures, into the objective is demonstrated. We present an exemplary optimization model for meanrisk optimization of an electricity portfolios of a price-taking retailer. Stochasticity enters the model via uncertain electricity demand, heat demand, spot prices, and future prices. The objective is to maximize the expected overall revenue and, simultaneously, to minimize risk in terms of multiperiod risk measures, i.e., risk measures that take into account intermediate cash values in order to avoid liquidity problems at any time. We compare the effect of different multiperiod polyhedral risk measures that had been suggested in our earlier work.