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

Worst-case estimation and asymptotic theory for models with unobservables

This paper proposes a worst-case approach for estimating econometric models containing unobservable variables. Worst-case estimators are robust against the adverse effects of unobservables. In contrast to the classical literature, there are no assumptions about the statistical nature of the unobservables in a worst-case estimation. This method is robust with respect to the unknown probability distribution of the unobservables and should be seen as a complement to standard methods, as cautious modelers should compare different estimations to determine robust models. The limit theory is obtained. A Monte Carlo study of finite sample properties has been conducted. An economic application is included

Valuation of boundary-linked assets

This article studies the valuation of boundary-linked assets and their derivatives in continuous-time markets. Valuing boundary-linked assets requires the solution of a stochastic differential equation with boundary conditions, which, often, is not Markovian. We propose a wavelet-collocation algorithm for solving a Milstein approximation to the stochastic boundary problem. Its convergence properties are studied. Furthermore, we value boundary-linked derivatives using Malliavin calculus and Monte Carlo methods. We apply these ideas to value European call options of boundary-linked asset

Computing continuous-time growth models with boundary conditions via wavelets

This paper presents an algorithm for approximating the solution of deterministic/stochastic continuous-time growth models based on the Euler's equation and the transversality conditions. The main issue for computing these models is to deal efficiently with the boundary conditions associated. This approach is a wavelets-collocation method derived from the finite-iterative trapezoidal approach. Illustrative examples are give

Existence and computation of a Cournot-Walras equilibrium

In this paper we present a general approach to existence problems in Cournot-Walras (CW) economies, based on mathematical programming theory. We propose a definition of the decision problem of firms which avoids the profit maximization rule as the only rational criterion for the firms and uses the excess demand function instead of the inverse demand function. We prove the existence of a CW equilibrium and we state practical conditions to characterize a CW equilibrium. We also propose efficient algorithms for computing CW equilibria. Finally, we consider some extensions such as externalities, Stackelberg, collusive and Nash equilibrium model

COMPUTING CONTINUOUS-TIME GROWTH MODELS WITH BOUNDARY CONDITIONS VIA WAVELETS

This paper presents an algorithm for approximating the solution of deterministic/stochastic continuous-time growth models based on the Euler's equation and the transversality conditions. The main issue for computing these models is to deal efficiently with the boundary conditions associated. This approach is a wavelets-collocation method derived from the finite-iterative trapezoidal approach. Illustrative examples are given.

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

VALUATION OF BOUNDARY-LINKED ASSETS

This article studies the valuation of boundary-linked assets and their derivatives in continuous-time markets. Valuing boundary-linked assets requires the solution of a stochastic differential equation with boundary conditions, which, often, is not Markovian. We propose a wavelet-collocation algorithm for solving a Milstein approximation to the stochastic boundary problem. Its convergence properties are studied. Furthermore, we value boundary-linked derivatives using Malliavin calculus and Monte Carlo methods. We apply these ideas to value European call options of boundary-linked assets.