A new proposition on the martingale representation theorem and on the approximate hedging of contingent claim in mean-variance criterion

In this work we revisit the problem of the hedging of contingent claim using mean-square criterion. We prove that in incomplete market, some probability measure can be identified so that becomes -martingale under .This is in fact a new proposition on the martingale representation theorem. The new results also identify a weight function that serves to be an approximation to the Radon-Nikodým derivative of the unique neutral martingale measure.

Cross-cultural dimensions of meaning in the evaluation of events in world history? Perceptions of historical calamities and progress in cross-cultural data from 30 societies

The universality versus culture specificity of quantitative evaluations (negative-positive) of 40 events in world history was addressed using World History Survey data collected from 5,800 university students in 30 countries/societies. Multidimensional scaling using generalized procrustean analysis indicated poor fit of data from the 30 countries to an overall mean configuration, indicating lack of universal agreement as to the associational meaning of events in world history. Hierarchical cluster analysis identified one Western and two non-Western country clusters for which adequate multidimensional fit was obtained after item deletions. A two-dimensional solution for the three country clusters was identified, where the primary dimension was historical calamities versus progress and a weak second dimension was modernity versus resistance to modernity. Factor analysis further reduced the item inventory to identify a single concept with structural equivalence across cultures, Historical Calamities, which included man-made and natural, intentional and unintentional, predominantly violent but also nonviolent calamities. Less robust factors were tentatively named as Historical Progress and Historical Resistance to Oppression. Historical Calamities and Historical Progress were at the individual level both significant and independent predictors of willingness to fight for one’s country in a hierarchical linear model that also identified significant country-level variation in these relationships. Consensus around calamity but disagreement as to what constitutes historical progress is discussed in relation to the political culture of nations and lay perceptions of history as catastrophe.

Super-resolution in confocal scanning microscopy: generalized inversion formulae

It was shown in previous papers that the resolution of a confocal scanning microscope can be significantly improved by measuring, for each scanning position, the full diffraction image and by inverting these data to recover the value of the object at the confocal point. In the present work, the authors generalize the data inversion procedure by allowing, for reconstructing the object at a given point, to make use of the data samples recorded at other scanning positions. This leads them to a family of generalized inversion formulae, either exact or approximate. Some previously known formulae are re-derived here as special cases in a particularly simple way.

Erratum: Generalized Smarr relation for Kerr-AdS black holes from improved surface integrals (Physical Review D (2005) 71 (044016)

SCOPUS: er.j