Minimal supersolutions of convex BSDEs

We study the nonlinear operator of mapping the terminal value $\xi$ to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in $y$, convex in $z$, jointly lower semicontinuous and bounded below by an affine function of the control variable $z$. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.Comment: Published in at http://dx.doi.org/10.1214/13-AOP834 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multivariate Shortfall Risk Allocation and Systemic Risk

The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the computation of an overall reserve level and its allocation to the different components according to their systemic relevance. We develop here a pragmatic approach to systemic risk measurement and allocation based on multivariate shortfall risk measures, where acceptable allocations are first computed and then aggregated so as to minimize costs. We analyze the sensitivity of the risk allocations to various factors and highlight its relevance as an indicator of systemic risk. In particular, we study the interplay between the loss function and the dependence structure of the components. Moreover, we address the computational aspects of risk allocation. Finally, we apply this methodology to the allocation of the default fund of a CCP on real data.Comment: Code, results and figures can also be consulted at https://github.com/yarmenti/MSR

Subjectivity in research: Why not ? But…

This article addresses the question of subjectivity in research. In order to facilitate the use of subjectivity in a research context, the author reminds readers of possible procedures as suggested in the literature. Particular attention is given to the idea of peer debriefing. Inspired by psychoanalysis, the author expands on the concept of discussant or debriefer and suggests that by doing so, subjectivity can be better understood. It is suggested that this may actually be fully integrated into a study in order to both better understand the subject under examination as well as the influence of the research mentor and student dyad. The author shares an example of this approach taken from a previously completed study on pedophile sex abusers

Dynamique sédimentaire des littoraux de l’estuaire du Saint-Laurent

Les marées, les vagues et la formation de la glace en hiver sont les principaux agents physiques de la dynamique sédimentaire des littoraux de l'estuaire du Saint-Laurent. La végétation joue un rôle déterminant dans la formation des schorres. L'estuaire du Saint-Laurent mesure 400 km de longueur, 70 km de largeur en aval et 15 km à la hauteur de l'île d'Orléans. Les dimensions de l'estuaire sont telles que les conditions hydrodynamiques qui prévalent en aval sont essentiellement marines, tandis que celles qui prévalent en amont sont typiquement estuariennes. La marée est de prédominance semi-diurne; le marnage est de 4,2 m à l'embouchure et atteint 7,5 m à l'autre extrémité. Les vagues peuvent atteindre une hauteur maximale de 4 m dans la région adjacente au golfe du Saint-Laurent et diminuent progressivement de hauteur vers l'amont selon la longueur des fetchs. La glace se forme en décembre dans l'estuaire et persiste jusqu'en avril. La glace joue un rôle très important dans l'estuaire du Saint-Laurent; elle transporte des sédiments de toutes tailles, des argiles jusqu'aux blocs, elle erode Ie schorre et la slikke, mais elle protège aussi le littoral de l'action des vagues. L'échange de sédiments entre le littoral et le large est un processus important, particulièrement dans la partie amont de l'estuaire où il est relié à des cycles saisonniers d'érosion et de sédimentation. Le taux élevé de sédimentation dans les ports révèle l'importance du transport de sédiments en suspension dans la zone côtière. L'aménagement hydro-électrique de plusieurs tributaires entrave l'apport naturel de sédiments alluviaux et provoque ainsi l'érosion des littoraux adjacents. La croissance des schorres est sous la dépendance de la végétation, ce qui rend ces derniers plus vulnérables à l'érosion à mesure qu'ils progressent en deçà du profil d'équilibre hydrodynamique. Excepté pour la présence de la glace, qui est particulière aux estuaires des régions froides, la dynamique sédimentaire des littoraux de l'estuaire du Saint-Laurent est comparable à celle des autres estuaires dans la mesure où l'on tient compte des grandes dimensions de l'estuaire du Saint-Laurent.Tides, waves and the formation of ice in winter are the principal physical agents of sediment dynamics in the St. Lawrence Estuary. Vegetation plays a predominant role in the building up of tidal marshes. The St. Lawrence Estuary is 400 km long, 70 km wide at the mouth and 15 km across at île d'Orléans. The dimensions of the Estuary are such that the hydrodynamic conditions prevailing in the lower portion are typically marine while those prevailing in the upper section are typically estuarine. The tide is semi-diurnal and reaches 4.2 m at the mouth and 7.5 m at the head of the estuary. Waves may reach a maximum height of 4 m in the region adjacent to the Gulf of St. Lawrence and they diminish progressively towards the head depending on fetch lengths. Ice forms in December and persists until April. Ice plays a very important role in the St. Lawrence Estuary; it transports sediments of all sizes, from clays to boulders, erodes tidal marshes and tidal flats but it also protects the intertidal zone from wave action. Onshore-offshore exchange of sediment is an important process, particularly in the upper portion of the estuary where it is linked to seasonal cycles of erosion and sedimentation. High sedimentation rates in harbours reveal the importance of the nearshore suspension load. The hydro-electric harnessing of many tributaries cuts the supply of sediments to adjacent littoral zones and induces erosion. The growth of tidal marshes is controled by the vegetation and they become more vulnerable to erosion as they depart from the hydrodynamic equilibrium profile. Except for the presence of ice which is particular to cold regions, nearshore sediment dynamics in the St. Lawrence Estuary are comparable to other estuaries when the large size of the St. Lawrence Estuary is taken into account