Network decomposition of general financial equilibria with transaction costs

In this paper, we developed a new general financial equilibrium model with transaction costs which considers multiple sectors of an economy, each of which seeks to determine its optimal composition of instruments held as assets and as liabilities in its portfolio. The governing equilibrium conditions are shown to satisfy a variational inequality problem, which is then studied in terms of existence and other qualitative properties. A decomposition algorithm is proposed which exploits the underlying generalized network structure of the problem and convergence results obtained. Finally, the algorithm is applied to compute the equilibrium asset, liability, and price pattern in several numerical examples.