A comparison principle for PDEs arising in approximate hedging problems: application to Bermudan options

In a Markovian framework, we consider the problem of finding the minimal initial value of a controlled process allowing to reach a stochastic target with a given level of expected loss. This question arises typically in approximate hedging problems. The solution to this problem has been characterised by Bouchard, Elie and Touzi in [1] and is known to solve an Hamilton-Jacobi-Bellman PDE with discontinuous operator. In this paper, we prove a comparison theorem for the corresponding PDE by showing first that it can be rewritten using a continuous operator, in some cases. As an application, we then study the quantile hedging price of Bermudan options in the non-linear case, pursuing the study initiated in [2]. [1] Bruno Bouchard, Romuald Elie, and Nizar Touzi. Stochastic target problems with controlled loss. SIAM Journal on Control and Optimization, 48(5):3123-3150,2009. [2] Bruno Bouchard, Romuald Elie, Antony R\'eveillac, et al. Bsdes with weak terminal condition. The Annals of Probability, 43(2):572-604,2015

A backward dual representation for the quantile hedging of Bermudan options

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of the pricing function. This algorithm is similar to the usual American backward induction, except that it requires two additional Fenchel transformations at each exercise date. We provide numerical illustrations

Invisible Minority: Experience of Middle Eastern American Women in Using Health Care Services

Issues related to the experiences of minority populations have received increasing attention during the last few decades. The research has been mostly focused on minority populations that are known to the U.S. general population including Hispanics, Asians, Native Americans, and African Americans. However, the Middle Eastern American population has received little attention. As the research on health disparities advances, there has been a growing attempt to reduce disparities that cause Middle Eastern populations to have chronic or life-threatening diseases. Some of these research studies have looked at the experiences of discrimination as a factor that would make a difference in the health of this population. While these studies are important, they usually engage a quantitative research method that is not fully equipped to evaluate the experiences of discrimination in a fuller sense. Addressing this gap in the literature, I conducted 30 in-depth interviews with Middle Eastern American women about their experiences with the U.S. health care system. Based on these interviews, there seem to be signs of anti-Middle Eastern racial framing among health care professionals that often caused significant problems for these respondents in their attempts to access the U.S. health care system

Characterization of lead-recycling facility emissions at various workplaces: Major insights for sanitary risks assessment

Most available studies on lead smelter emissions deal with the environmental impact of outdoor particles, but only a few focus on air quality at workplaces. The objective of this study is to physically and chemically characterize the Pb-rich particles emitted at different workplaces in a lead recycling plant. A multiscale characterization was conducted from bulk analysis to the level of individual particles, to assess the particles properties in relation with Pb speciation and availability. Process PM from various origins were sampled and then compared; namely Furnace and Refining PM respectively present in the smelter and at refinery workplaces, Emissions PM present in channeled emissions. These particles first differed by their morphology and size distribution, with finer particles found in emissions. Differences observed in chemical composition could be explained by the industrial processes. All PM contained the same major phases (Pb, PbS, PbO, PbSO4 and PbO·PbSO4) but differed on the nature and amount of minor phases. Due to high content in PM, Pb concentrations in the CaCl2 extractant reached relatively high values (40mgL−1). However, the ratios (soluble/total) of CaCl2 exchangeable Pb were relatively low (<0.02%) in comparison with Cd (up to 18%). These results highlight the interest to assess the soluble fractions of all metals (minor and major) and discuss both total metal concentrations and ratios for risk evaluations. In most cases metal extractability increased with decreasing size of particles, in particular, lead exchangeability was highest for channeled emissions. Such type of study could help in the choice of targeted sanitary protection procedures and for further toxicological investigations. In the present context, particular attention is given to Emissions and Furnace PM. Moreover, exposure to other metals than Pb should be considered

Recovery and reuse of discontinuous carbon fibres by solvolysis: Realignment and properties of remanufactured materials

Discontinuous carbon fibre tows were recovered after solvolysis of an aeronautic type composite made with RTM6 epoxy resin. A Sohxlet extraction method was used to quantify the organic residue on the fibre tows and showed that less than 3 wt% was remaining on the surface. The recovered tows were therefore reused directly to manufacture a plate with randomly distributed carbon fibres and then three plates with realigned carbon fibres. The latter were then characterised and tested and the results obtained were compared to the material manufactured using the same type of virgin fibres by the same method. The materials made from recycled carbon fibres showed very good properties in comparison to the virgin fibre material, despite the presence of flaws such as quality of the fibre surface after solvolysis, alignment and voids). This is the first time in the open literature that carbon fibres recovered from solvolysis were reused in this way together with characterisation of the resulting materials

Regular poly(para-phenylene) films bound to gold surfaces through the electrochemical reduction of diazonium salts followed by electropolymerization in an ionic liquid

International audienceBy combining the electroreduction of diazonium salts and the electropolymerization of conducting polymers in an ionic liquid, the electrografting of a regular poly(para-phenylene) film on a gold substrate is achieved, leading to the strong and robust anchoring of the PPP polymers on the substrate (Au-PPP hybrid). A thin layer covalently bound to the substrate is first prepared by the reduction of benzenediazonium salt (BD), then, on top of this layer, a thicker layer of poly(para-phenylene) (PPP) is easily grown by the electrochemical oxidation of biphenyl in the [BMIm][PF6] ionic liquid. The resulting material is thoroughly characterized by IR, ToF-SIMS and fluorescence spectroscopies. The analyses show the formation of well regular PPP layers that are wired to the substrate. The key role of the [BMIm][PF6] ionic liquid in the structuration of the polymer is emphasized

Détection de primitives linéaires et circulaires par une approche a contrario

National audienceLow-level image understanding requires the use of different detectors for basic primitives, such as line segments or circular arcs. Most of the existent detectors deal with problems that have been (and still are) extensively studied like parameter tunning, control of number of false detections or execution time. In this paper, we focus on detecting simultaneously lines and circles in an image, while controlling the number of false detections and without any need of parameter tunning. We present an algorithm which extends the Line Segment Detector (LSD) for circles, both being based on the a contrario approach. Due to the fact that the proposed detector targets two different types of primitives, the a contrario validation is used as a criterion for model selection, which is a novelty in the a contrario-based works. In addition, we propose a new algebraic method for estimating a circle, which benefits equally from the direction of the gradient of the contour points, and not only from their position.La compréhension bas niveau d'une image exige l'usage des différents détecteurs de primitives de base, telles que des segments de droite ou arcs de cercles. La plupart des détecteurs existants se confrontent à des problèmes qui ont été (et sont toujours) considérablement étudiés comme le réglage de paramètres, le contrôle du nombre de fausses détections ou le temps d'exécution. Dans cet article, nous nous intéressons à la détection à la fois des droites et des cercles dans une image, tout en contrôlant le nombre de fausses détections et sans réglage particulier de paramètres. Nous présentons un détecteur qui étend l'algorithme LSD (Line Segment Detector) aux cercles, les deux étant fondés sur une approche a contrario. Du fait que le détecteur proposé vise deux types différents de primitives, la validation a contrario est utilisée comme méthode de sélection du modèle, ce qui représente une nouveauté dans les travaux fondés sur l'approche a contrario. De plus, nous proposons une nouvelle méthode d'estimation algébrique d'un cercle, qui profite également de la direction du gradient des points contour, et non pas uniquement de la position de ceux-ci

Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN)

International audienceWhile permeability scaling of fractured media has been so far studied independently at the fracture- and network- scales, we propose a numerical analysis of the combined effect of fracture-scale heterogeneities and the network-scale topology. The analysis is based on 2 106 discrete fracture network (DFNs) simulations performed with highly robust numerical methods. Fracture local apertures are distributed according to a truncated Gaussian law, and exhibit self-affine spatial correlations up to a cutoff scale Lc. Network structures range widely over sparse and dense systems of short, long or widely distributed fracture sizes and display a large variety of fracture interconnections, flow bottlenecks and dead-ends. At the fracture scale, accounting for aperture heterogeneities leads to a reduction of the equivalent fracture transmissivity of up to a factor of 6 as compared to the parallel plate of identical mean aperture. At the network scale, a significant coupling is observed in most cases between flow heterogeneities at the fracture and at the network scale. The upscaling from the fracture to the network scale modifies the impact of fracture roughness on the measured permeability. This change can be quantified by the measure a2, which is analogous to the more classical power-averaging exponent used with heterogeneous porous media, and whose magnitude results from the competition of two effects: (i) the permeability is enhanced by the highly transmissive zones within the fractures that can bridge fracture intersections within a fracture plane; (ii) it is reduced by the closed and low transmissive areas that break up connectivity and flow paths. Citation: de Dreuzy, J.-R., Y. Méheust, and G. Pichot (2012), Influence of fracture scale heterogeneit