Solving the non-convexity problem in some shopping-time and human-capital models

Several works in the shopping-time and in the human-capital literature, due to the nonconcavity of the underlying Hamiltonian, use Örst-order conditions in dynamic optimization to characterize necessity, but not su¢ ciency, in intertemporal problems. In this work I choose one paper in each one of these two areas and show that optimality can be characterized by means of a simple aplication of Arrowís (1968) su¢ ciency theorem.

Affine processes, arbitrage-Free Term structures of legendre polynomials,and option pricing

Multivariate Affine term structure models have been increasingly used for pricing derivatives in fixed income markets. In these models, uncertainty of the term structure is driven by a state vector, while the short rate is an affine function of this vector. The model is characterized by a specific form for the stochastic differential equation (SDE) for the evolution of the state vector. This SDE presents restrictions on its drift term which rule out arbitrages in the market. In this paper we solve the following inverse problem: Suppose the term structure of interest rates is modeled by a linear combination of Legendre polynomials with random coefficients. Is there any SDE for these coefficients which rules out arbitrages? This problem is of particular empirical interest because the Legendre model is an example of factor model with clear interpretation for each factor, in which regards movements of the term structure. Moreover, the Affine structure of the Legendre model implies knowledge of its conditional characteristic function. From the econometric perspective, we propose arbitrage-free Legendre models to describe the evolution of the term structure. From the pricing perspective, we follow Duffie et al. (2000) in exploring Legendre conditional characteristic functions to obtain a computational tractable method to price fixed income derivatives. Closing the article, the empirical section presents precise evidence on the reward of implementing arbitrage-free parametric term structure models: The ability of obtaining a good approximation for the state vector by simply using cross sectional data.

Entry and externality : hydroelectric generators in Brazil

This work analyzes the entry problem in the hydroelectric generation industry. The operation of a generator upstream regularizes the river flow for generators located downstream on the same river, increasing the production capacity of the latter. This positive externality increases the attractiveness of the locations downstream whenever a generator decides to enter upstream. Therefore, the entry decision of a generator in a given location may affect all entry decisions in potential locations for plants downstream. I first model the problem of generators located in cascade on the same river to show the positive effect of the externality. Next, I develop a method to estimate an entry model specific to the hydro generation industry which takes into account the externality of the entry decisions. Finally, I use a data set on investment decisions of Brazilian hydro-generators to estimate the model. The results show a positive incentive to locate downstream from existing plants and from locations where entry is likely to occur. An interesting by-product of the analysis is that the year effects’ estimates show an increase one year before the energy crisis of 2001, providing evidence that the market anticipated the crisis. It contradicts the governmental version that the crisis was due to an unexpected drought.

The risk-incentive trade-off in competitive search

Usando a abordagem de competitive search, modelo um mercado de trabalho com trabalhadores heterogêneos no qual há um problema de risco moral na relação entre firmas e trabalhadores. Nesse contexto, consigo prever como contratos reagem a mudanças nos parâmetros do mercado (em particular, o risco de produção), assim como a variação da probabilidade dos trabalhadores serem contratados. Minha contribuição principal é ver que, no nível individual, existe uma relação negativa entre risco e incentivos, mas efeitos de equilíbrio geral implicam que essa relação pode ser positiva no nível agregado. Esse resultado ajuda a esclarecer resultados empíricos contraditórios sobre a relação entre risco e incentivos.