A New Class Of Models For Stochastic Complementarity Problems

In this paper, we study a new class of models for stochastic complementarity problems (SCP) based on risk measurement. By taking merit function or equivalent function for SCP as risk function, we construct the optimization problems to measure the risk induced by employing SCP models. We consider two cases:1. By using Lagrangian implicit function as risk function, we model the SCP based on conditional value-at-risk (CVaR) problems. Moreover, we present the deterministic approximation problems by introducing smoothing techniques and Monte Carlo sampling techniques, then the convergency analysis is given. Second, for the same risk function, we further consider the SCP based on worst-case CVaR (WCVaR) problems, especially WCVaR under mixture distribution uncertainty. In a similar way, we formulate the approximation problems and give the convergency results.2. By talking a max function which is defined on non-negative space as risk function, we consider linear SCP based on the WCVaR under box uncertainty and ellipsoidal uncer-tainty. We first introduce the equivalent minimization problems and claim that they are convex optimization problems under some conditions. Then we illustrate the problems with two preliminary examples.