Deviation measures in stochastic programming with mixed-integer recourse

This thesis aims to contribute to the systematic measurement of risk in decision problems under uncertainty. In particular, we intend to support the choice of a risk measure in stochastic linear programming with mixed-integer recourse. We restrict our discussion to deviation measures which include in our terminology such frequently used risk measures as the standard deviation, the standard semideviation, the absolute semideviation, and the expected excess of a fixed target. The choice among risky alternatives is one major issue in decision theory. We review the axiomatic approaches of stochastic dominance orders and coherent risk measures. Then, we discuss deviation measures and the associated meanrisk models in the context of these concepts. A mean-risk model is a bicriteria optimization problem on a family of random variables. In stochastic programming, the random variables are linked by a cost function. We provide a general view on the underlying decision problem, derive results on the structure and the stability of the mean-risk models from the structure of the cost function, and apply these results to stochastic programming with recourse. More precisely, we conclude properties concerning the continuity and the convexity of the optimal value functions and concerning the qualitative stability of the optimization problems. These properties lead to different implications for the different deviation measures. We investigate stochastic programs with and without integer variables but focus on the former ...