  The stochastic variational inequality problem (SVIP) is an equilibrium model
that includes random variables and has been widely applied in various fields
such as economics and engineering. Expected residual minimization (ERM) is an
established model for obtaining a reasonable solution for the SVIP, and its
objective function is an expected value of a suitable merit function for the
SVIP. However, the ERM is restricted to the case where the distribution is
known in advance. We extend the ERM to ensure the attainment of robust
solutions for the SVIP under the uncertainty distribution (the extended ERM is
referred to as distributionally robust expected residual minimization (DRERM),
where the worst-case distribution is derived from the set of probability
measures in which the expected value and variance take the same sample mean and
variance, respectively). Under suitable assumptions, we demonstrate that the
DRERM can be reformulated as a deterministic convex nonlinear semidefinite
programming to avoid numerical integration.
