Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Improving the risk concept: a revision of Arrow-Pratt theory in the context of controlled dynamic stochastic environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic �complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous.

Note on a theorem of Bousfield and Friedlander

We examine the proof of a classical localization theorem of Bousfield and Friedlander and we remove the assumption that the underlying model category be right proper. The key to the argument is a lemma about factoring in morphisms in the arrow category of a model category.

Stochastic dominance and absolute risk aversion

In this paper we proose the infimum of the Arrow-Pratt index of absoluterisk aversion as a measure of global risk aversion of a utility function.We then show that, for any given arbitrary pair of distributions, thereexists a threshold level of global risk aversion such that all increasingconcave utility functions with at least as much global risk aversion wouldrank the two distributions in the same way. Furthermore, this thresholdlevel is sharp in the sense that, for any lower level of global riskaversion, we can find two utility functions in this class yielding oppositepreference relations for the two distributions.

Valuation bubbles and sequential bubbles

Price bubbles in an Arrow-Debreu valuation equilibrium in infinite-timeeconomy are a manifestation of lack of countable additivity of valuationof assets. In contrast, known examples of price bubbles in sequentialequilibrium in infinite time cannot be attributed to the lack of countableadditivity of valuation. In this paper we develop a theory of valuation ofassets in sequential markets (with no uncertainty) and study the nature ofprice bubbles in light of this theory. We consider an operator, calledpayoff pricing functional, that maps a sequence of payoffs to the minimumcost of an asset holding strategy that generates it. We show that thepayoff pricing functional is linear and countably additive on the set ofpositive payoffs if and only if there is no Ponzi scheme, and providedthat there is no restriction on long positions in the assets. In the knownexamples of equilibrium price bubbles in sequential markets valuation islinear and countably additive. The presence of a price bubble indicatesthat the asset's dividends can be purchased in sequential markers at acost lower than the asset's price. We also present examples of equilibriumprice bubbles in which valuation is nonlinear but not countably additive.

Analysis of leakage properties and guiding conditions of rib antiresonant reflecting optical waveguides

Power leakage properties and guiding conditions of rib antiresonant reflecting optical waveguides (rib-ARROW) have been theoretically and experimentally studied as a function of wavelength and polarization of the light for different geometrical and optical parameters that characterize the rib-ARROW structure. Obtained results show that rib-ARROWs can only be fabricated with low losses in a wavelength range when determined rib configurations are adopted. Furthermore, these waveguides exhibit a polarization sensitivity that largely depends on the core-substrate refractive index difference. Together with the experimental results, theoretical calculations from different modeling methods are also presented and discussed.

Majorization arrow in quantum-algorithm design

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.

Intersecciones entre visión artificial y mirada artística. Semantic Intersections between Artificial and Artistic Vision.

En el presente artículo se ha desarrollado un sistema capaz de categorizar de forma automática la base de datos de imágenes que sirven de punto de partida para la ideación y diseño en la producción artística del escultor M. Planas. La metodología utilizada está basada en características locales. Para la construcción de un vocabulario visual se sigue un procedimiento análogo al que se utiliza en el análisis automático de textos (modelo 'Bag-of-Words'-BOW) y en el ámbito de las imágenes nos referiremos a representaciones 'Bag-of-Visual Terms' (BOV). En este enfoque se analizan las imágenes como un conjunto de regiones, describiendo solamente su apariencia e ignorando su estructura espacial. Para superar los inconvenientes de polisemia y sinonimia que lleva asociados esta metodología, se utiliza el análisis probabilístico de aspectos latentes (PLSA) que detecta aspectos subyacentes en las imágenes, patrones formales. Los resultados obtenidos son prometedores y, además de la utilidad intrínseca de la categorización automática de imágenes, este método puede proporcionar al artista un punto de vista auxiliar muy interesante.