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 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.

Brand value in horizontal alliances : the case of twin-cars.

Rival firms often cooperate horizontally in order to share risks and achieve scale advantages in production or in their research and development projects. The output of these strategic alliances is usually sold by the individual ally company under its own brand and using its own marketing mix strategies. Marketing strategies create a cumulative effect that is reflected in brand value. Although horizontal alliances often have a significant overall impact on firm profitability, undesired brand value dilution is a worrisome possibility for the partners and therefore a relevant subject of study. In this paper, we consider brand value to be the economic added value of a brand, and propose two marketbased measures of brand value: (1) price premia (which are relevant for a unit sale) and (2) revenue premia (which also account for the premia in sales volume). We apply this analysis to the Spanish market for new automobiles, in which successful and long-lasting horizontal alliances have formed. Our findings suggest that, during the introduction stage of the product life cycle, horizontal allies did not charge different price premia, but that horizontal allies profit from differences in brand reputation obtained from demand side effects such as revenue premia (specifically, the impact on sales volume). Consequently, horizontal cooperation among brands does not dilute their value at the introduction stage. Furthermore, our results suggest that horizontal allies do charge different price premia during the growth stage of the product life cycle. Consequently, horizontal allies have recognized strategies that do not dilute brand value in intense competition mitigating the brand value diluting riskBrand value; Revenue premia; Automobile market; Price premia; Marketing;

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

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

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

Solving dynamic stochastic economic models by mathematical programming decomposition methods.

Discrete-time optimal control problems arise naturally in many economic problems. Despite the rapid growth in computing power and new developments in the literature, many economic problems are still quite challenging to solve. Economists are aware of the limitations of some of these approaches for solving these problems due to memory and computational requirements. However, many of the economic models present some special structure that can be exploited in an efficient manner. This paper introduces a decomposition methodology, based on a mathematical programming framework, to compute the equilibrium path in dynamic models by breaking the problem into a set of smaller independent subproblems. We study the performance of the method solving a set of dynamic stochastic economic models. The numerical results reveal that the proposed methodology is efficient in terms of computing time and accuracyDynamic stochastic economic model; Computation of equilibrium; Mathematical programming; Decomposition techniques;

When giving some away makes sense to jump-start the diffusion process.

This paper uses an analytical model to examine when it makes sense to provide incentives to innovators to adopt a new product. The model allows for separate segments of innovators and imitators, each of which follows a Bass-type diffusion process. Interestingly “seeding” the market is optimal for a limited range of situations and these do not appear to include those where there is a downturn in sales (chasm) as sales move from the first to the second segment. Research has frequently identified different segments of adopters of new products. Categorizations include innovators vs imitators (Bass, 1969; Rogers, 1995; Mahahan et al., 1990; Im et al., 2003), technophiles vs “normal” people, and business vs consumer users. Further, considerable effort has gone into studying the influence of members of the first group on the second. This paper focuses on when, if ever, it makes sense for a manufacture of a new product to “seed” the market by subsidizing a few early adopters to speed the adoption process. The paper builds on earlier work by Kalish and Lilien (1983) which focused on the impact of widely available government subsidies on the adoption of socially desirable innovations (i.e. alternative energy sources) as well as the work of Jain et al. (1995). Unlike that work, we concentrate on providing subsidies (here free goods) to selective individuals in the context of a model which allows for separate segments of innovators and imitators and nests the standard Bass (1969) model.

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

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