On the optimal investment

In 1988 Dybvig introduced the payoff distribution pricing model (PDPM) as an alternative to the capital asset pricing model (CAPM). Under this new paradigm agents preferences depend on the probability distribution of the payoff and for the same distribution agents prefer the payoff that requires less investment. In this context he gave the notion of efficient payoff. Both approaches run parallel to the theory of choice of von Neumann -Morgenstern (1947), known as the Expected Utility Theory and posterior axiomatic alternatives. In this paper we consider the notion of optimal payoff as that maximizing the terminal position for a chosen preference functional and we investigate the relationship between both concepts, optimal and efficient payoffs, as well as the behavior of the efficient payoffs under different market dynamics. We also show that path-dependent options can be efficient in some simple models

Haplotypes of the bovine IgG2 heavy gamma chain in tick-resistant and tick-susceptible breeds of cattle

Bovines present contrasting, heritable phenotypes of infestations with the cattle tick, Rhipicephalus (Boophilus) microplus. Tick salivary glands produce IgG-binding proteins (IGBPs) as a mechanism for escaping from host antibodies that these ectoparasites ingest during blood meals. Allotypes that occur in the constant region of IgG may differ in their capacity to bind with tick IGBPs; this may be reflected by the distribution of distinct allotypes according to phenotypes of tick infestations. In order to test this hypothesis, we investigated the frequency of haplotypes of bovine IgG2 among tick-resistant and tick-susceptible breeds of bovines. Sequencing of the gene coding for the heavy chain of IgG2 from 114 tick-resistant (Bos taurus indicus, Nelore breed) and tick-susceptible (B. t. taurus, Holstein breed) bovines revealed SNPs that generated 13 different haplotypes, of which 11 were novel and 5 were exclusive of Holstein and 3 of Nelore breeds. Alignment and modeling of coded haplotypes for hinge regions of the bovine IgG2 showed that they differ in the distribution of polar and hydrophobic amino acids and in shape according to the distribution of these amino acids. We also found that there was an association between genotypes of the constant region of the IgG2 heavy chain with phenotypes of tick infestations. These findings open the possibility of investigating if certain IgG allotypes hinder the function of tick IGBPs. If so, they may be markers for breeding for resistance against tick infestations

Gene Expression Profiling in Limb-Girdle Muscular Dystrophy 2A

Limb-girdle muscular dystrophy type 2A (LGMD2A) is a recessive genetic disorder caused by mutations in calpain 3 (CAPN3). Calpain 3 plays different roles in muscular cells, but little is known about its functions or in vivo substrates. The aim of this study was to identify the genes showing an altered expression in LGMD2A patients and the possible pathways they are implicated in. Ten muscle samples from LGMD2A patients with in which molecular diagnosis was ascertained were investigated using array technology to analyze gene expression profiling as compared to ten normal muscle samples. Upregulated genes were mostly those related to extracellular matrix (different collagens), cell adhesion (fibronectin), muscle development (myosins and melusin) and signal transduction. It is therefore suggested that different proteins located or participating in the costameric region are implicated in processes regulated by calpain 3 during skeletal muscle development. Genes participating in the ubiquitin proteasome degradation pathway were found to be deregulated in LGMD2A patients, suggesting that regulation of this pathway may be under the control of calpain 3 activity. As frizzled-related protein (FRZB) is upregulated in LGMD2A muscle samples, it could be hypothesized that β-catenin regulation is also altered at the Wnt signaling pathway, leading to an incorrect myogenesis. Conversely, expression of most transcription factor genes was downregulated (MYC, FOS and EGR1). Finally, the upregulation of IL-32 and immunoglobulin genes may induce the eosinophil chemoattraction explaining the inflammatory findings observed in presymptomatic stages. The obtained results try to shed some light on identification of novel therapeutic targets for limb-girdle muscular dystrophies

Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups

International audienceWhen performing statistics on elements of sets that possess a particular geometric structure, it is desirable to respect this structure. For instance in a Lie group, it would be judicious to have a notion of a mean which is stable by the group operations (composition and inversion). Such a property is ensured for Riemannian center of mass in Lie groups endowed with a bi-invariant Riemannian metric, like compact Lie groups (e.g. rotations). However, bi-invariant Riemannian metrics do not exist for most non compact and non-commutative Lie groups. This is the case in particular for rigid-body transformations in any dimension greater than one, which form the most simple Lie group involved in biomedical image registration. In this paper, we propose to replace the Riemannian metric by an affine connection structure on the group. We show that the canonical Cartan connections of a connected Lie group provides group geodesics which are completely consistent with the composition and inversion. With such a non-metric structure, the mean cannot be defined by minimizing the variance as in Riemannian Manifolds. However, the characterization of the mean as an exponential barycenter gives us an implicit definition of the mean using a general barycentric equation. Thanks to the properties of the canonical Cartan connection, this mean is naturally bi-invariant. We show the local existence and uniqueness of the invariant mean when the dispersion of the data is small enough. We also propose an iterative fixed point algorithm and demonstrate that the convergence to the invariant mean is at least linear. In the case of rigid-body transformations, we give a simple criterion for the global existence and uniqueness of the bi-invariant mean, which happens to be the same as for rotations. We also give closed forms for the bi-invariant mean in a number of simple but instructive cases, including 2D rigid transformations. For general linear transformations, we show that the bi-invariant mean is a generalization of the (scalar) geometric mean, since the determinant of the bi-invariant mean is the geometric mean of the determinants of the data. Finally, we extend the theory to higher order moments, in particular with the covariance which can be used to define a local bi-invariant Mahalanobis distance