Approximation theory for stochastic variational and Ky Fan inequalities in finite dimensions

The ideas of approximation and continuity have been extensively investigated both for optimization problems and varational inequalities. This paper studies approximation issues for a class of VIs, called Stochastic Variational Inequalities (SVIs), that arise, for example, in stochastic programming and portfolio choice problems. SVI problems are special cases of a more general class of problems that it will study first, called Stochastic Ky Fan Inequalities (SKFIs). The paper also analyzes the role of monotonicity in the analysis of both SVIs and SKFIs. The present interest in these problems is motivated by recent research in the theory of portfolio choice for investors who are not classical expected utility maximizers.