Sharp convex bounds on the aggregate sums--An alternative proof

It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that comonotonic risks have the convex-largest sum, ASTIN Bulletin 32, 71-80. Cheung (2010), Characterizing a comonotonic random vector by the distribution of the sum of its components, Insurance: Mathematics and Economics 47(2), 130-136] and that a random vector with given marginal distributions is mutually exclusive if and only if it has the minimal convex sum [Cheung and Lo (2014), Characterizing mutual exclusivity as the strongest negative multivariate dependence structure, Insurance: Mathematics and Economics 55, 180-190]. In this note, we give a new proof of this two results using the theories of distortion risk measure and expected utility.Comment: 11page

Joint Mixability of Elliptical Distributions and Related Families

In this paper, we further develop the theory of complete mixability and joint mixability for some distribution families. We generalize a result of R\"uschendorf and Uckelmann (2002) related to complete mixability of continuous distribution function having a symmetric and unimodal density. Two different proofs to a result of Wang and Wang (2016) which related to the joint mixability of elliptical distributions with the same characteristic generator are present. We solve the Open Problem 7 in Wang (2015) by constructing a bimodal-symmetric distribution. The joint mixability of slash-elliptical distributions and skew-elliptical distributions is studied and the extension to multivariate distributions is also investigated.Comment: 15page

The Effect of Education on Marital Status and Partner Characteristics: Evidence from the UK

This paper uses a particular school exit rule previously in effect in England and Wales that allowed students born within the first five months of the academic year to leave school one term earlier than those born later in the year. Focusing on women, we show that those who were required to stay on an extra term more frequently hold some academic qualification. Using having been required to stay on as an exogenous factor affecting academic attainment, we find that holding a (low level) academic qualification has no effect on a women's probability of being married, but increases the probability of her husband holding some academic qualification and being economically active.education, marriage, assortative mating