AN INTERIOR POINT ALGORITHM FOR COMPUTING EQUILIBRIA IN ECONOMIES WITH INCOMPLETE ASSET MARKETS

Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalogue of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. We prove that the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, we solve relevant examples of GEI markets.

An interior point algorithm for computing equilibria in economies with incomplete asset markets

Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalogue of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. We prove that the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, we solve relevant examples of GEI market

An interior-point algorithm for computing equilibria in economies with incomplete asset markets

Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalog of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. It is proved that, under mild conditions, the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, relevant examples of GEI markets are solvedPublicad

Existence and computation of a GEI equilibrium

In this paper we propose a general mathematical approach to existence of production equilibria in general economic model with incomplete assets markets, based on mathematical programming theory. In the first part, we demonstrate the existence of a General Equilibrium with Incomplete markets (GEl)}. In the second part, we introduce a concept of local equilibrium and we characterize such an equilibrium as the solution of a nonlinear system of equations. This system is very useful in practice since we avoid to compute the excess demand function that is difficult to obtain in large applied models. Furthermore, our characterization only requires limited short-selling and convexity assumptions at the neighborhood of the solution point. Finally, we also propose an algorithm for computing equilibria by interior point methods and we present numerical examples

Incomplete-Market Equilibria Solved Recursively on an Event Tree

We develop a method that allows one to compute incomplete-market equilibria routinely for Markovian equilibria (when they exist). The main difficulty to be overcome arises from the set of state variables. There are, of course, exogenous state variables driving the economy but, in an incomplete market, there are also endogenous state variables, which introduce path dependence. We write on an event tree the system of all first-order conditions of all times and states and solve recursively for state prices, which are dual variables. We illustrate this "dual" method and show its many practical advantages by means of several examples.