Longevity Risk and Capital Markets: The 2015-16 Update

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An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12]

Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection.Comment: 36 page

Magnetism: the Driving Force of Order in CoPt. A First-Principles Study

CoPt or FePt equiatomic alloys order according to the tetragonal L10 structure which favors their strong magnetic anisotropy. Conversely magnetism can influence chemical ordering. We present here {\it ab initio} calculations of the stability of the L10 and L12 structures of Co-Pt alloys in their paramagnetic and ferromagnetic states. They show that magnetism strongly reinforces the ordering tendencies in this system. A simple tight-binding analysis allows us to account for this behavior in terms of some pertinent parameters

Page number not for citation purposes 1 Des Furoncles résistants aux antibiotiques: penser à la myiase !!

Les myiases sont des infections parasitaires par des larves de mouches. La localisation cutanée doit être évoquée de retour d'un pays tropical devant une évolution inhabituelle de lésions cutanées. Nous rapportons une observation d'un militaire tunisien, ayant séjourné en République Démocratique du Congo. Il était atteint de myiase cutanée simulatrice d'une furonculose résistante aux antibiotiques. L'intérêt de cette observation est de souligner l'importance d'évoquer la myiase dont le traitement est simple et rapide chez un patient de retour de zone d'endémie.Key words: Furoncles, myiase, mouche

Nmrk2 gene is upregulated in dilated cardiomyopathy and required for cardiac function and nad levels during aging

Dilated cardiomyopathy (DCM) is a disease of multifactorial etiologies, the risk of which is increased by male sex and age. There are few therapeutic options for patients with DCM who would benefit from identification of common targetable pathways. We used bioinformatics to identify the Nmrk2 gene involved in nicotinamide adenine dinucleotde (NAD) coenzyme biosynthesis as activated in different mouse models and in hearts of human patients with DCM while the Nampt gene controlling a parallel pathway is repressed. A short NMRK2 protein isoform is also known as muscle integrin binding protein (MIBP) binding the α7β1 integrin complex. We investigated the cardiac phenotype of Nmrk2-KO mice to establish its role in cardiac remodeling and function. Young Nmrk2-KO mice developed an eccentric type of cardiac hypertrophy in response to pressure overload rather than the concentric hypertrophy observed in controls. Nmrk2-KO mice developed a progressive DCM-like phenotype with aging, associating eccentric remodeling of the left ventricle and a decline in ejection fraction and showed a reduction in myocardial NAD levels at 24 months. In agreement with involvement of NMRK2 in integrin signaling, we observed a defect in laminin deposition in the basal lamina of cardiomyocytes leading to increased fibrosis at middle age. The α7 integrin was repressed at both transcript and protein level at 24 months. Nmrk2 gene is required to preserve cardiac structure and function, and becomes an important component of the NAD biosynthetic pathways during aging. Molecular characterization of compounds modulating this pathway may have therapeutic potential