On classical set-compatibility

In this paper, I generalise the logical concept of compatibility into a broader set-theoretical one. The basic idea is that two sets are incompatible if they produce at least one pair of opposite objects under some operation. I formalise opposition as an operation ′ ∶ E → E, where E is the set of opposable elements of our universe U, and I propose some models. From this, I define a relation ℘U × ℘U × ℘U^℘U, which has (mutual) logical compatibility as its more natural interpretation

Credit Constraints and Macroeconomic Instability in a Small Open Economy

This paper presents a dynamic model for a small open economy with imperfect financial market. It provides a framework to analyze the role of credit constraints and debt denomination in the generation and amplification of macroeconomic instability in an open economy context. As in Bernanke and Gertler (1989), the imperfection in the financial market results from the existence of a costly state of verification (CSV) problem. Entrepreneurs whose net worth is not enough to finance their desired physical investment have to pay a premium above the risk-free interest rate to obtain external funds. Other key ingredients of the model are that a foreign good is used as an input in the production of the capital good, and that the debt is denominated in terms of the foreign good. Real exchange rate depreciations generate an increase in the cost of producing capital and a reduction in the net worth of entrepreneurs due to the debt denomination. Therefore, recessionary effects can be deepenedExchange rates, credit constraints, open economy.

INTEREST RATES, PROMOTIONAL PRIZES AND COMPETITION IN THE BANKING INDUSTRY

Some Colombian commercial banks have used the strategy of offering promotional prizes in order to attract new savings customers. In this paper we develop a two-stage game model that allows us to understand the efects of this romotional strategy on the deposit interest rates, the deposit market shares and the intermediation spreads. We find that under this strategy it is possible for the bank that ofers the highest prize to segment the deposit market serving only customers that assign high subjective probabilities to winning prizes. More importantly we show that the bank that ofers the highest promotional prize not only pays the lowest deposit interest rate but also has the largest deposit market share and the widest intermediation spread.Banking Competition

Tropicalization and irreducibility of Generalized Vandermonde Determinants

We find geometric and arithmetic conditions in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix over the algebraic closure of any field k. We also characterize those determinants whose tropicalization with respect to the variables of a row is irreducible.Comment: 10 pages, AMSart. Revised version to appear in Proceedings of the AM

Computing Vertex Centrality Measures in Massive Real Networks with a Neural Learning Model

Vertex centrality measures are a multi-purpose analysis tool, commonly used in many application environments to retrieve information and unveil knowledge from the graphs and network structural properties. However, the algorithms of such metrics are expensive in terms of computational resources when running real-time applications or massive real world networks. Thus, approximation techniques have been developed and used to compute the measures in such scenarios. In this paper, we demonstrate and analyze the use of neural network learning algorithms to tackle such task and compare their performance in terms of solution quality and computation time with other techniques from the literature. Our work offers several contributions. We highlight both the pros and cons of approximating centralities though neural learning. By empirical means and statistics, we then show that the regression model generated with a feedforward neural networks trained by the Levenberg-Marquardt algorithm is not only the best option considering computational resources, but also achieves the best solution quality for relevant applications and large-scale networks. Keywords: Vertex Centrality Measures, Neural Networks, Complex Network Models, Machine Learning, Regression ModelComment: 8 pages, 5 tables, 2 figures, version accepted at IJCNN 2018. arXiv admin note: text overlap with arXiv:1810.1176

A social stigma model of child labor

This paper constructs a model in which a social norm is internalized. The social disapproval of people who violate the norm -stigmatization-- is incorporated as a reduction in their utility. That reduction in utility is lower as the proportion of the population that violates the norm increases. In the model, society disapproves of people sending their children to work and parents care about that “embarrassment”. An equilibrium is constructed in which the expected and realized stigma costs are the same; and the wages rates of child and adult labor are such as to equate demand and supply for each kind of labor.