Determination of general equilibrium with incomplete markets and default penalties

This paper is concerned with the existence and computation of general equilibrium with incomplete asset markets and default. Due to the incompleteness of asset markets, the excess demand functions are typically not continuous at prices and delivery rates for which the assets have redundant nominal deliveries. This discontinuity results in a serious problem for the existence and computation of general equilibrium. We show that this problem can be resolved by replacing the nominal delivery matrix with a constant-rank one and restricting the macro variables in a subset of the domains. With this approach, the economies with incomplete markets and default penalties can be analyzed with differentiable homotopy techniques, and thus in the same framework as standard general equilibrium models. As a by-product, the existence of equilibrium is ensured for generic economies. Several computational examples demonstrate the effectiveness of the algorithm and show some quantitative features of equilibria in the model with default penalties.