On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Banning information as a redistributive device

In this paper we analyze the optimality of allowing firms to observe signals of workers’ characteristics in an optimal taxation framework. We show that it is always optimal to prohibit signals that disclose information about differences in the intrinsic productivities of workers like mandatory health exams and IQ tests, for example. On the other hand, it is never optimal to forbid signals that reveal information about the comparative advantages of workers like their specialization and profession. When signals are mixed (they disclose both types of information), there is a trade-off between efficiency and equity. It is optimal to prohibit signals with sufficiently low comparative advantage content.

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.

On choice of technique in the Robinson-Solow-Srinivasan model

We report results on the optimal \choice of technique" in a model originally formulated by Robinson, Solow and Srinivasan (henceforth, the RSS model) and further discussed by Okishio and Stiglitz. By viewing this vintage-capital model without discounting as a speci c instance of the general theory of intertemporal resource allocation associated with Brock, Gale and McKenzie, we resolve longstanding conjectures in the form of theorems on the existence and price support of optimal paths, and of conditions suÆcient for the optimality of a policy rst identi ed by Stiglitz. We dispose of the necessity of these conditions in surprisingly simple examples of economies in which (i) an optimal path is periodic, (ii) a path following Stiglitz' policy is bad, and (iii) there is optimal investment in di erent vintages at di erent times. (129 words)

Two additions to Lucas's "inflation and welfare"

This work adds to Lucas (2000) by providing analytical solutions to two problems that are solved only numerically by the author. The first part uses a theorem in control theory (Arrow' s sufficiency theorem) to provide sufficiency conditions to characterize the optimum in a shopping-time problem where the value function need not be concave. In the original paper the optimality of the first-order condition is characterized only by means of a numerical analysis. The second part of the paper provides a closed-form solution to the general-equilibrium expression of the welfare costs of inflation when the money demand is double logarithmic. This closed-form solution allows for the precise calculation of the difference between the general-equilibrium and Bailey's partial-equilibrium estimates of the welfare losses due to inflation. Again, in Lucas's original paper, the solution to the general-equilibrium-case underlying nonlinear differential equation is done only numerically, and the posterior assertion that the general-equilibrium welfare figures cannot be distinguished from those derived using Bailey's formula rely only on numerical simulations as well.

Parcerias público-privadas na presença de seleção adversa: uma análise numérica

Esta dissertação propõe-se a analisar a otimalidade de parcerias público-privadas (PPP) em um ambiente de seleção adversa. Mais especi calmente, analiso se as tarefas de construir e operar uma infraestrutura para serviços públicos deve ser realizada por um consórcio ou se devem ser realizadas por fi rmas contratadas separadamente. Para tal, diferentemente da literatura existente para o problema, focadas nos problemas de contratos incompletos e moral hazard, construo um modelo de seleção adversa multidimensional, onde as firrmas possuem informação privada e podem exercer um esforço não observável em cada atividade, com a existência de externalidade entre as tarefas, em uma extensão do modelo de La¤ont e Tirole (1986). Após defi nir algumas condições sob as quais PPP domina os meios usuais de contratação, utilizo de uma análise numérica para melhor compreender a solução do modelo, que se mostra altamente dependente da correlação entre os parâmetros de informação privada das firmas.

Exact arbitrage, well-diversified portfolios and asset pricing in large markets

: In a model of a nancial market with an atomless continuum of assets, we give a precise and rigorous meaning to the intuitive idea of a \well-diversi ed" portfolio and to a notion of \exact arbitrage". We show this notion to be necessary and su cient for an APT pricing formula to hold, to be strictly weaker than the more conventional notion of \asymptotic arbitrage", and to have novel implications for the continuity of the cost functional as well as for various versions of APT asset pricing. We further justify the idealized measure-theoretic setting in terms of a pricing formula based on \essential" risk, one of the three components of a tri-variate decomposition of an asset's rate of return, and based on a speci c index portfolio constructed from endogenously extracted factors and factor loadings. Our choice of factors is also shown to satisfy an optimality property that the rst m factors always provide the best approximation. We illustrate how the concepts and results translate to markets with a large but nite number of assets, and relate to previous work.

Are one-sided S,s rules useful proxies for optimal pricing rules?

This article is motivated by the prominence of one-sided S,s rules in the literature and by the unrealistic strict conditions necessary for their optimality. It aims to assess whether one-sided pricing rules could be an adequate individual rule for macroeconomic models, despite its suboptimality. It aims to answer two questions. First, since agents are not fully rational, is it plausible that they use such a non-optimal rule? Second, even if the agents adopt optimal rules, is the economist committing a serious mistake by assuming that agents use one-sided Ss rules? Using parameters based on real economy data, we found that since the additional cost involved in adopting the simpler rule is relatively small, it is plausible that one-sided rules are used in practice. We also found that suboptimal one-sided rules and optimal two-sided rules are in practice similar, since one of the bounds is not reached very often. We concluded that the macroeconomic effects when one-sided rules are suboptimal are similar to the results obtained under two-sided optimal rules, when they are close to each other. However, this is true only when one-sided rules are used in the context where they are not optimal.

Private or public? a taxonomy of optimal ownership and management regimes

We develop a theory of public versus private ownership based on value diversion by managers. Government is assumed to face stronger institutional constraints than has been assumed in previous literature. The model which emerges from these assumptions is fexible and has wide application. We provide amapping between the qualitative characteristics of an asset, its main use - including public goods characteristics, and spillovers toother assets values - and the optimal ownership and management regime. The model is applied to single and multiple related assets. We address questions such as; when is it optimal to have one of a pair ofr elated assets public and the other private; when is joint management desirable; and when should a public asset be managed by the owner of a related private asset? We show that while private ownership can be judged optimal in some cases solely on the basis of qualitative information, the optimality of any other ownership and management regimes relies on quantitative analysis. Our results reveal the situations in which policy makers will have difficulty in determining the opimal regime.

On Ponzi schemes in infinite horizon collateralized economies with default penalties

Araujo, Páscoa and Torres-Martínez (2002) showed that, without imposing any debt constraint, Ponzi schemes are ruled out in infinite horizon economies with limited commitment when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2009) presented two examples in which they argued that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. Moreover, they claimed that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is restored. This paper questions the validity of the claims made in Páscoa and Seghir (2009). First, we show that it is not true that harsh default penalties lead to Ponzi schemes in the examples they have proposed. A competitive equilibrium with no trade can be supported due to unduly pessimistic expectations on asset deliveries. We subsequently refine the equilibrium concept in the spirit of Dubey, Geanakoplos and Shubik (2005) in order to rule out spurious inactivity on asset markets due to irrational expectations. Our second contribution is to provide a specific example of an economy with moderate default penalties in which Ponzi schemes reappear when overpessimistic beliefs on asset deliveries are ruled out. Our finding shows that, contrary to what is claimed by Páscoa and Seghir (2009), moderate default penalties do not always prevent agents to run a Ponzi scheme.

Essays on monetary and banking theory

Esta tese de Doutorado é dedicada ao estudo de instabilidade financeira e dinâmica em Teoria Monet ária. E demonstrado que corridas banc árias são eliminadas sem custos no modelo padrão de teoria banc ária quando a popula ção não é pequena. É proposta uma extensão em que incerteza agregada é mais severa e o custo da estabilidade financeira é relevante. Finalmente, estabelece-se otimalidade de transições na distribui ção de moeda em economias em que oportunidades de trocas são escassas e heterogêneas. Em particular, otimalidade da inflação depende dos incentivos dinâmicos proporcionados por tais transi ções. O capí tulo 1 estabelece o resultado de estabilidade sem custos para economias grandes ao estudar os efeitos do tamanho populacional na an álise de corridas banc árias de Peck & Shell. No capí tulo 2, otimalidade de dinâmica é estudada no modelo de monet ário de Kiyotaki & Wright quando a sociedade é capaz de implementar uma polí tica inflacion ária. Apesar de adotar a abordagem de desenho de mecanismos, este capí tulo faz um paralelo com a an álise de Sargent & Wallace (1981) ao destacar efeitos de incentivos dinâmicos sobre a interação entre as polí ticas monet ária e fiscal. O cap ítulo 3 retoma o tema de estabilidade fi nanceira ao quanti car os custos envolvidos no desenho ótimo de um setor bancário à prova de corridas e ao propor uma estrutura informacional alternativa que possibilita bancos insolventes. A primeira an álise mostra que o esquema de estabilidade ótima exibe altas taxas de juros de longo prazo e a segunda que monitoramento imperfeito pode levar a corridas bancárias com insolvência.

Approximate recursive equilibrium with minimal state space

This paper shows existence of approximate recursive equilibrium with minimal state space in an environment of incomplete markets. We prove that the approximate recursive equilibrium implements an approximate sequential equilibrium which is always close to a Magill and Quinzii equilibrium without short sales for arbitrarily small errors. This implies that the competitive equilibrium can be implemented by using forecast statistics with minimal state space provided that agents will reduce errors in their estimates in the long run. We have also developed an alternative algorithm to compute the approximate recursive equilibrium with incomplete markets and heterogeneous agents through a procedure of iterating functional equations and without using the rst order conditions of optimality.

A study of the impacts of quantitative easing on the macroeconomics variables

Neste trabalho, propusemos um modelo DSGE que busca responder algumas questões sobre políticas de afrouxamento monetário (Quantitative Easing - QE) recentemente implementadas em resposta à crise de 2008. Desenvolvemos um modelo DSGE com agentes heterogêneos e preferred-habitat nas compras de títulos do governo. Nosso modelo permite o estudo da otimalidade da compra de portfolio (em termos de duration dos títulos) para os bancos centrais quando estão implementando a política. Além disso, a estrutura heterogênea nos permite olhar para distribuição de renda provocada pelas compras de títulos. Nossos resultados preliminares evidenciam o efeito distributivo do QE. No entanto, nosso modelo expandido apresentou alguns problemas de estabilidade.

Ensaios em Finanças

Esta tese é composta de três artigos sobre finanças. O primeiro tem o título "Nonparametric Option Pricing with Generalized Entropic Estimators " e estuda um método de apreçamento de derivativos em mercados incompletos. Este método está relacionado com membros da família de funções de Cressie-Read em que cada membro fornece uma medida neutra ao risco. Vários testes são feitos. Os resultados destes testes sugerem um modo de definir um intervalo robusto para preços de opções. Os outros dois artigos são sobre anúncios agendados em diferentes situações. O segundo se chama "Watching the News: Optimal Stopping Time and Scheduled Announcements" e estuda problemas de tempo de parada ótimo na presença de saltos numa data fixa em modelos de difusão com salto. Fornece resultados sobre a otimalidade do tempo de parada um pouco antes do anúncio. O artigo aplica os resultados ao tempo de exercício de Opções Americanas e ao tempo ótimo de venda de um ativo. Finalmente o terceiro artigo estuda um problema de carteira ótima na presença de custo fixo quando os preços podem saltar numa data fixa. Seu título é "Dynamic Portfolio Selection with Transactions Costs and Scheduled Announcement" e o resultado mais interessante é que o comportamento do investidor é consistente com estudos empíricos sobre volume de transações em momentos próximos de anúncios.

Essays on incentives, procurement and regulation

Esta tese é composta de três artigos. No primeiro artigo, "Simple Contracts under Simultaneous Adverse Selection and Moral Hazard", é considerado um problema de principal-agente sob a presença simultânea dos problemas de risco moral e seleção adversa, em que a dimensão de seleção adversa se dá sobre as distribuições de probabilidade condicionais as ações do agente. No segundo artigo, "Public-Private Partnerships in the Presence of Adverse Selection" é analisada a otimalidade de parcerias público-privadas sob a presença de seleção adversa. No terceiro artigo, "Regulation Under Stock Market Information Disclosure", por sua vez, é considerado o problema da regulação de firmas de capital aberto, onde as firmas possuem incentivos para mandar sinais opostos para o regulador e o mercado.