WCVaR-based Formulation For Stochastic Variational Inequality Problems

This paper has studied a kind of new model for solving the stochastic variational inequality. In recent years, stochastic variational inequalities has been receiving much attention, and measures of risk play a crucial role in optimization under uncertainty. It has been used in many fields, especially the control of financial risk.Inspired by the previous work, we use the Worst case Condition Value-at-Risk (WC-VaR) to solve the stochastic variational inequality problems by reducing the risk. First, we put forward a new model, and then transform it into a convex program problem under suitable conditions. After that, We analyze the boundedness of the model’s level set. We also propose a smoothing approximation method by using the Monte Carlo techniques and a smoothing technical for finding a solution of the new reformulation. we prove the convergence under some conditions. Finally some numerical experiments indicate that the proposed method is suitable.