A New Approach to Computing Equilibrium in Incomplete Markets

The paper is a sequel to Won (2016) which attempts to characterize full-rank GEI equilibrium as pre-GEI equilibrium. The pre-GEI equilibrium ap-proach for computing full-rank GEI equilibrium is useful because pre-GEI equi-librium always exist under standard conditions. The goal of the current paper is to develop algorithms which can be implemented to compute pre-GEI equilib-rium. The algorithms are built on a prototype system of equations which consist of the first-order conditions for utility maximization and market clearing condi-tions. The prototype system can be directly encoded into an algorithm or can be transformed into implementable forms for algorithms such as homotopy path-following algorithms. Two examples are presented where the algorithms are implemented to compute pre-GEI equilibrium and their performance are com-paratively discussed.