Polynomial approximations for bivariate aggregate claims amount probability distributions

A numerical method to compute bivariate probability distributions from their Laplace transforms is presented. The method consists in an orthogonal projection of the probability density function with respect to a probability measure that belongs to a Natural Exponential Family with Quadratic Variance Function (NEF-QVF). A particular link to Lancaster probabilities is highlighted. The procedure allows a quick and accurate calculation of probabilities of interest and does not require strong coding skills. Numerical illustrations and comparisons with other methods are provided. This work is motivated by actuarial applications. We aim at recovering the joint distribution of two aggregate claims amounts associated with two insurance policy portfolios that are closely related, and at computing survival functions for reinsurance losses in presence of two non-proportional reinsurance treaties

Longevity Risk and Capital Markets: The 2015-16 Update

International audienc

In Utero Diagnosis of Niemann-Pick Type C in the Absence of Family History

Niemann-Pick type C (NPC) disease is a recessive disorder that results in unesterified cholesterol accumulating in the lysosomal and late endosomal system. It is caused by mutations in NPC1 or NPC2 genes and leads to systemic and neurodegenerative symptoms. Few cases of prenatal presentation of NPC have been reported and only two cases in the absence of previous family history, indicating the diagnosis is particularly difficult in such a situation. We report a prenatal diagnosis of NPC in a couple without family history. An ultrasound screening at 22 weeks of gestation (WG) detected fetal ascites and hepatomegaly, which were still present at 25, 27, and 29 WG, and a splenomegaly progressively appeared. No placentomegaly or other signs of hydrops fetalis were observed. The diagnostic of NPC was prenatally confirmed by a filipin test and NPC1 sequencing and multiplex ligation-dependent probe amplification assay which revealed a maternal missense mutation (c.2608T>C; p.Ser870Pro) and a paternal deletion of exons 5 to 25. This additional prenatal case of NPC suggests that even in the absence of family history, fetal ascites associated with splenomegaly but no hydrops should nonetheless arouse suspicion concerning this disease as a possible diagnosis

The Force-Velocity Relation for Growing Biopolymers

The process of force generation by the growth of biopolymers is simulated via a Langevin-dynamics approach. The interaction forces are taken to have simple forms that favor the growth of straight fibers from solution. The force-velocity relation is obtained from the simulations for two versions of the monomer-monomer force field. It is found that the growth rate drops off more rapidly with applied force than expected from the simplest theories based on thermal motion of the obstacle. The discrepancies amount to a factor of three or more when the applied force exceeds 2.5kT/a, where a is the step size for the polymer growth. These results are explained on the basis of restricted diffusion of monomers near the fiber tip. It is also found that the mobility of the obstacle has little effect on the growth rate, over a broad range.Comment: Latex source, 9 postscript figures, uses psfig.st

Insurance: Models, Digitalization, and Data Science

International audienc