Variational inequalities in the analysis and computation of multi-sector, multi-instrument financial equilibria☆

Abstract In this paper, a general model of competitive financial equilibrium is developed with multiple sectors and multiple instruments that can be held as assets and/or as liabilities. The model assumes that the economic behavior of each sector is that of utility maximization and yields the equilibrium asset, liability, and price pattern. The variational inequality formulation of the equilibrium conditions is first derived and then utilized to investigate qualitative properties of the equilibrium pattern. A computational procedure is proposed for the solution of the model and convergence results given. The algorithm decomposes the variational inequality problem into series of quadratic programming problems. Finally, a numerical example is given to illustrate the algorithm.

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