Análise de portfólio: uma perspectiva bayesiana

Este trabalho tem com objetivo abordar o problema de alocação de ativos (análise de portfólio) sob uma ótica Bayesiana. Para isto foi necessário revisar toda a análise teórica do modelo clássico de média-variância e na sequencia identificar suas deficiências que comprometem sua eficácia em casos reais. Curiosamente, sua maior deficiência não esta relacionado com o próprio modelo e sim pelos seus dados de entrada em especial ao retorno esperado calculado com dados históricos. Para superar esta deficiência a abordagem Bayesiana (modelo de Black-Litterman) trata o retorno esperado como uma variável aleatória e na sequência constrói uma distribuição a priori (baseado no modelo de CAPM) e uma distribuição de verossimilhança (baseado na visão de mercado sob a ótica do investidor) para finalmente aplicar o teorema de Bayes tendo como resultado a distribuição a posteriori. O novo valor esperado do retorno, que emerge da distribuição a posteriori, é que substituirá a estimativa anterior do retorno esperado calculado com dados históricos. Os resultados obtidos mostraram que o modelo Bayesiano apresenta resultados conservadores e intuitivos em relação ao modelo clássico de média-variância.

Central limit theorem for asymmetric kernel functionals

Asymmetric kernels are quite useful for the estimation of density functions with bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. These asymmetric kernels are nonnegative and free of boundary bias. Moreover, their shape varies according to the location of the data point, thus also changing the amount of smoothing. This paper applies the central limit theorem for degenerate U-statistics to compute the limiting distribution of a class of asymmetric kernel functionals.

A note on an application of Arrow's theorem: sufficient conditions for Lucas' inflation and welfare

Bellman's methods for dynamic optimization constitute the present mainstream in economics. However, some results associated with optimal controI can be particularly usefuI in certain problems. The purpose of this note is presenting such an example. The value function derived in Lucas' (2000) shopping-time economy in Infiation and Welfare need not be concave, leading this author to develop numerical analyses to determine if consumer utility is in fact maximized along the balanced path constructed from the first order conditions. We use Arrow's generalization of Mangasarian's results in optimal control theory and develop sufficient conditions for the problem. The analytical conclusions and the previous numerical results are compatible .

On the Impossibility of an Exact Imperfect Monitoring Folk Theorem

It is shown that, for almost every two-player game with imperfect monitoring, the conclusions of the classical folk theorem are false. So, even though these games admit a well-known approximate folk theorem, an exact folk theorem may only be obtained for a measure zero set of games. A complete characterization of the efficient equilibria of almost every such game is also given, along with an inefficiency result on the imperfect monitoring prisoner s dilemma.

Local concavifiability of preferences and determinacy of equilibrium

In this paper we consider strictly convex monotone continuous complete preorderings on R+n that are locally representable by a concave utility function. By Alexandroff 's (1939) theorem, this function is twice dífferentiable almost everywhere. We show that if the bordered hessian determinant of a concave utility representation vanishes on a null set. Then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of c1 manifolds. This property of consumer demand is enough to guarantee that the equilibrium prices of apure exchange economy will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the Katzner (1968) - Debreu (1970, 1972) smoothness conditions.

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 a uniform turnpike of the third kind in the Robinson-Solow-Srinivasan model

On using McKenzie’s taxonomy of optimal accumulation in the longrun, we report a “uniform turnpike” theorem of the third kind in a model original to Robinson, Solow and Srinivasan (RSS), and further studied by Stiglitz. Our results are presented in the undiscounted, discrete-time setting emphasized in the recent work of Khan-Mitra, and they rely on the importance of strictly concave felicity functions, or alternatively, on the value of a “marginal rate of transformation”, ξσ, from one period to the next not being unity. Our results, despite their specificity, contribute to the methodology of intertemporal optimization theory, as developed in economics by Ramsey, von Neumann and their followers.

The ex-Ante non-optimality of the Dempster-Schafer updating rule for ambiguous beliefs

The most widely used updating rule for non-additive probalities is the Dempster-Schafer rule. Schmeidles and Gilboa have developed a model of decision making under uncertainty based on non-additive probabilities, and in their paper “Updating Ambiguos Beliefs” they justify the Dempster-Schafer rule based on a maximum likelihood procedure. This note shows in the context of Schmeidler-Gilboa preferences under uncertainty, that the Dempster-Schafer rule is in general not ex-ante optimal. This contrasts with Brown’s result that Bayes’ rule is ex-ante optimal for standard Savage preferences with additive probabilities.

Oligopolistic competition under knightian uncertainty

This artic/e applies a theorem of Nash equilibrium under uncertainty (Dow & Werlang, 1994) to the classic Coumot model of oligopolistic competition. It shows, in particular, how one can map all Coumot equilibrium (which includes the monopoly and the null solutions) with only a function of uncertainty aversion coefficients of producers. The effect of variations in these parameters over the equilibrium quantities are studied, also assuming exogenous increases in the number of matching firms in the game. The Cournot solutions under uncertainty are compared with the monopolistic one. It shows principally that there is an uncertainty aversion level in the industry such that every aversion coefficient beyond it induces firms to produce an aggregate output smaller than the monopoly output. At the end of the artic/e equilibrium solutions are specialized for Linear Demand and for Coumot duopoly. Equilibrium analysis in the symmetric case allows to identify the uncertainty aversion coefficient for the whole industry as a proportional lack of information cost which would be conveyed by market price in the perfect competition case (Lerner Index).

A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

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.

Pure strategy equilibria of multidimensional and non-monotonic auctions

We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in interdependent values auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and sufficient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results can give a new justification to the use of tournaments in practice.

Environmental protection and economic growth

This paper explores the link between environmental policy and economic growth by employing an extension of the AK Growth Model. We include a state equation for renewable natural resources. We assume that the change in environmental regulations induces costs and that economic agents also derive some utility from capital stock accumulation vis-`a-vis the environment. Using the Hopf bifurcation theorem, we show that cyclical environmental policy strategies are optimal, providing theoretical support for the Environmental Kuznets Curve.

Escolha social e valores irredutíveis: uma aproximação da economia política e a ideologia

No presente paper, nós provamos que qualquer função da escolha social satisfaz o princípio da independência das alternativas irrelevantes (IIA) de Arrow se o comportamento individual é menu-dependente. Portanto, o 'Teorema da Possibilidade Geral' de Arrow não é válido quando as preferências individuais são determinadas por valores irredutíveis. Nesse contexto, qualquer instrumento de agregação que satisfaça os princípios não-ditatoriais e paretianos de unanimidade (maioria simples, por exemplo) também faz IIA. Esse poderia ser um resultado importante para a teoria da escolha social, enquanto um comportamento individual determinado por valores irredutíveis (interesse próprio, ideologia, Ética e normas sociais, por exemplo) podendo validar democracia representativa. A importância relativa de tais valores e da possibilidade de reversão da preferência determina a dinâmica da escolha social, de acordo com os princípios democráticos.