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Economic equilibrium through variational inequalities

Magdalena Nockowska-Rosiak (2009)

Applicationes Mathematicae

The purpose of this paper is to present an alternative proof of the existence of the Walrasian equilibrium for the Arrow-Debreu-McKenzie model by the variational inequality technique. Moreover, examples of the generalized Arrow-Debreu-McKenzie model are given in which the price vector can reach the boundary of the orthant allowing a commodity to be of price zero at equilibrium. In such a case its supply exceeds demand. It is worth mentioning that utility functions in this model are allowed not to...

Économie et théorie des catastrophes

Yves Balasko (1978)

Mathématiques et Sciences Humaines

Les hypothèses de différentiabilité jouent un rôle essentiel dans plusieurs travaux récents consacrés à l'étude des propriétés de l'équilibre économique. Cet article présente une synthèse aussi élémentaire que possible d'une partie de ces travaux et fait aussi le lien avec la théorie des catastrophes de Thom.

Edge-disjoint odd cycles in graphs with small chromatic number

Claude Berge, Bruce Reed (1999)

Annales de l'institut Fourier

For a simple graph, we consider the minimum number of edges which block all the odd cycles and the maximum number of odd cycles which are pairwise edge-disjoint. When these two coefficients are equal, interesting consequences appear. Similar problems (but interchanging “vertex-disjoint odd cycles” and “edge-disjoint odd cycles”) have been considered in a paper by Berge and Fouquet.

Eigenanalysis and metric multidimensional scaling on hierarchical structures.

Carles Maria Cuadras, Josep-Maria Oller (1987)

Qüestiió

The known hierarchical clustering scheme is equivalent to the concept of ultrametric distance. Every distance can be represented in a spatial model using multidimensional scaling. We relate both classes of representations of proximity data in an algebraic way, obtaining some results and relations on clusters and the eigenvalues of the inner product matrix for an ultrametric distance. Principal coordinate analysis on an ultrametric distance gives two classes of independent coordinates, describing...

El índice de poder de Banzhaf en la Unión Europea ampliada.

Encarnación Algaba Durán, Jesús Mario Bilbao Arrese, Julio Rodrigo Fernández García, Jorge Jesús López Vázquez (2001)

Qüestiió

En este trabajo se definen algoritmos, basados en funciones generatrices, para calcular el índice de poder de Banzhaf en juegos simples de votación ponderada y en juegos de doble y triple mayoría. La utilización de funciones generatrices permite un cálculo exacto del índice de Banzhaf con una reducción sensible de la complejidad temporal. Además se calculan los índices de Banzhaf para las reglas de decisión, aprobadas en la cumbre de Niza, que se utilizarán en la Unión Europea ampliada a 27 países....

El potencial de Hart y Mas-Colell para juegos restringidos por grafos.

J. M. Bilbao Arrese, Jorge López Vázquez (1996)

Qüestiió

This paper analyzes a model of formation of connected coalitions in a cooperative game. This model is a communication situation, and the Shapley value of this graph-restricted game is the Myerson value. The potential function for cooperative games was defined by Hart and Mas-Colell, and Winter showed that the Myerson value admits a potential function. We study a recursive procedure for computing the potential of the Myerson value. In section 3, we use the Myerson value for measuring voting power...

El problema de selección de la cartera en un mercado logarítmico-normal con criterio de utilidad R-ε.

Eduardo Ramos Méndez (1983)

Trabajos de Estadística e Investigación Operativa

Se estudia el problema de selección de la cartera bajo la hipótesis de que las rentas de los títulos individuales y de las carteras siguen distribuciones logarítmico-normales empleando como criterio de ordenación del conjunto de carteras el criterio de utilidad del riesgo fijado R-ε. Se proporciona el modo de obtener la cartera correspondiente a cada nivel de riesgo, así como el subconjunto de carteras eficientes.

Elementary Introduction to Stochastic Finance in Discrete Time

Peter Jaeger (2012)

Formalized Mathematics

This article gives an elementary introduction to stochastic finance (in discrete time). A formalization of random variables is given and some elements of Borel sets are considered. Furthermore, special functions (for buying a present portfolio and the value of a portfolio in the future) and some statements about the relation between these functions are introduced. For details see: [8] (p. 185), [7] (pp. 12, 20), [6] (pp. 3-6).

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