SCHRIFTENREIHE DER FAKULTÄT FÜR MATHEMATIK A Note on Stability for Risk Averse Stochastic Complementarity Problems by

Introduced by Chen and Fukushima in 2005, expected residual minimization (ERM) has become an established approach to complementarity problems under stochastic uncertainty. NCP and merit functions allow to recast deterministic complementarity problems as optimization problems, where the objective function is the total residual. Based on this reformulation, the risk neutral ERM formulation aims to minimize the expectation of the total residual. In the present work, we propose an extension of the ERM formulation by replacing the expectation with a more general convex, nondecreasing and law-invariant risk functional. Our model allows to take risk aversion into account. We examine joint continuity of the objective function with respect to both, the decision and the probability measure induced by the entering random vector. The latter allows to investigate the problem’s behavior when working with approximations of the original distribution. We consider perturbations of the underlying probability measure with respect to the weak topology and derive a stability of the optimal value function and the optimal solution set mapping. The paper concludes with demonstrating that our assumptions hold for almost all practically relevant NCP functions.