Search results for "Mathematical Economics"

Uncertainty Measures, Realizations and Entropies*

1997

This paper presents the axiomatic foundations of uncertainty theories arising in quantum theory and artificial intelligence. Plausibility measures and additive uncertainty measures are investigated. The representation of uncertainty measures by random sets in spaces of events forms a common base for the treatment of an appropriate integration theory as well as for a reasonable decision theory.

A Pedagogical Proof of Arrow's Impossibility Theorem

1999

In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 133=2197 possible combinations of the three individuals' rational preferences. However, by considering the subset of linear preferences, and employing the full strength of the IIA axiom, I reduce the number of cases necessary to completely describe the SWF to a small number, allowing an elementary proof suitable for most undergraduate students. This special case conveys the nature of Arrow's result. It is well known that the restriction to three options is not really limiting (any larger se…

Axiomatic characterization of the weighted solidarity values

2014

Abstract We define and characterize the class of all weighted solidarity values . Our first characterization employs the classical axioms determining the solidarity value (except symmetry ), that is, efficiency , additivity and the A-null player axiom , and two new axioms called proportionality and strong individual rationality . In our second axiomatization, the additivity and the A-null player axioms are replaced by a new axiom called average marginality .

Some dissenting views on the transitivity of individual preference

1990

(1) The transitivity property is not a necessary condition for the rationality of all individual preference relations. (2) A weakened definition of the transitivity is not necessarily relevant. (3) The non-transitivity of fuzzy preference relations is not inconsistent with a fuzzy total preorder structure on the set of alternatives.

Swing options in commodity markets: a multidimensional Lévy diffusion model

2013

Author's version of an article in the journal: Mathematical Methods of Operations Research. Also available from the publisher at: http://dx.doi.org/10.1007/s00186-013-0452-7 We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constraint. We analyze some general properties of the model and study the solution by analyzing the associated HJB-equation. Furthermo…

Is bad mathematics useless?

2008

The Classical Notion of Competition Revisited

2013

This article seeks to fill a lacuna within classical economics concerning the process of market price determination in situations of market disequilibrium. To this aim, first we distinguish the classical notion of free competition from the Walrasian notion of perfect competition and we argue that the latter is beset with some theoretical difficulties alien to the former. Second, we reconstruct in some detail Smith’s and Marx’s views concerning market price determination and show that Marx’s extensive use of metaphors and numerical examples foreshadows the modern taxonomy of buyers’ market, sellers’ market, and mixed strategy equilibrium in the capacity space of a standard Bertrand duopoly m…

On factor decomposition of cross-country income inequality: some extensions and qualifications

2001

Abstract In a recent paper in this journal Duro and Esteban [Econom. Lett. 60 (1998) 269] have proposed a factor decomposition of the Theil [Economics and Information Theory, Amsterdam, North-Holland, 1967] index of inequality over per capita incomes into the (unweighted) sum of the inequality indexes of the factors in order to measure the contribution of each individual factor to the overall inequality. The purpose of this little note is to extend and qualify the meaning of such a decomposition, to show that the decomposition also holds for another Theil [Economics and Information Theory, Amsterdam, North-Holland, 1967], index of inequality and that both decompositions offer qualitatively …

Measuring Social Mobility

1993

Abstract The paper considers the ranking of mobility matrices in a simple Markov model of social mobility. The approach is the dynamic counterpart ot the "static" inequality ranking of income distributions by the Lorenz curve. The derived partial ordering is motivated by welfare considerations, is shown to be equivalent to same intuitive mobility concepts, and is used to screen some immobility indices. The equivalence of the ranking with the "permanent income" Lorenz ordering gives support to the claim that this approach is the natural extension of Kolm′s [The optimal production of social justice, in "Public Economics (J. Margolis and H. Guitton, Eds.), MacMillan, London, 1969], Atkinson′s …

Inference for Lorenz curve orderings

1999

In this paper we consider the issue of performing statistical inference for Lorenz curve orderings. This involves testing for an ordered relationship in a multivariate context and making comparisons among more than two population distributions. Our approach is to frame the hypotheses of interest as sets of linear inequality constraints on the vector of Lorenz curve ordinates, and apply order-restricted statistical inference to derive test statistics and their sampling distributions. We go on to relate our results to others which have appeared in recent literature, and use Monte Carlo analysis to highlight their respective properties and comparative performances. Finally, we discuss in gener…