On Nested Affine Variational Inequalities: The Case of Multi-Portfolio Selection

We deal with nested affine variational inequalities, i.e., hierarchical problems involving an affine (upper-level) variational inequality whose feasible set is the solution set of another affine (lower-level) variational inequality. We apply this modeling tool to the multi-portfolio selection problem, where the lower-level variational inequality models the Nash equilibrium problem made up by the different accounts, while the upper-level variational inequality is instrumental to perform a selection over this equilibrium set. We propose a projected averaging Tikhonov-like algorithm for the solution of this problem, which only requires the monotonicity of the variational inequalities for both the upper- and the lower-level in order to converge. Finally, we provide complexity properties.