Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth

The theory of Forward-Backward Stochastic Differential Equations (FBSDEs) paves a way to probabilistic numerical methods for nonlinear parabolic PDEs. The majority of the results on the numerical methods for FBSDEs relies on the global Lipschitz assumption, which is not satisfied for a number of important cases such as the Fisher--KPP or the FitzHugh--Nagumo equations. Furthermore, it has been shown in \cite{LionnetReisSzpruch2015} that for BSDEs with monotone drivers having polynomial growth in the primary variable $y$, only the (sufficiently) implicit schemes converge. But these require an additional computational effort compared to explicit schemes. This article develops a general framework that allows the analysis, in a systematic fashion, of the integrability properties, convergence and qualitative properties (e.g.~comparison theorem) for whole families of modified explicit schemes. The framework yields the convergence of some modified explicit scheme with the same rate as implicit schemes and with the computational cost of the standard explicit scheme. To illustrate our theory, we present several classes of easily implementable modified explicit schemes that can computationally outperform the implicit one and preserve the qualitative properties of the solution to the BSDE. These classes fit into our developed framework and are tested in computational experiments.Comment: 49 pages, 3 figure

Some results on general quadratic reflected BSDEs driven by a continuous martingale

AbstractWe study the well-posedness of general reflected BSDEs driven by a continuous martingale, when the coefficient f of the driver has at most quadratic growth in the control variable Z, with a bounded terminal condition and a lower obstacle which is bounded above. We obtain the basic results in this setting: comparison and uniqueness, existence, stability. For the comparison theorem and the special comparison theorem for reflected BSDEs (which allows one to compare the increasing processes of two solutions), we give intrinsic proofs which do not rely on the comparison theorem for standard BSDEs. This allows to obtain the special comparison theorem under minimal assumptions. We obtain existence by using the fixed point theorem and then a series of perturbations, first in the case where f is Lipschitz in the primary variable Y, and then in the case where f can have slightly-superlinear growth and the case where f is monotonous in Y with arbitrary growth. We also obtain a local Lipschitz estimate in BMO for the martingale part of the solution

Subtonal features in a three-tone language: Evidence from Laal

In this paper, I provide arguments in favor of subtonal features, with data from Laal, an endangered, three-tone isolate language of southern Chad. I show that a system using the two features [upper] and [raised] (Yip 1980, Pulleyblank 1986) offers a straightforward account of properties of the Mid tone that are otherwise impossible to account for using the three tonal primitives H, M, L. I show that Laal provides evidence for parallels between tonal and segmental behavior which justify a featural analysis of tone. In particular, Laal displays a tonal assimilation process involving natural classes of subtonal features, which works just like vowel harmony, and could be described as a form of tone harmony. This goes against arguments frequently put forward against subtonal features (e.g. Hyman 2010, Patin et al. 2010). Additionally, the Laal case shows that the featural specification of the M tone in three-height tone systems is not necessarily ambiguous, making subtonal features potentially well-suited for the analysis of tone systems of all shapes

Phantom structure: A representational account of floating tone association

This paper focuses on the association of floating tones. One type we call "phonological association", where the tone-bearing unit (TBU) the floating tone associates to is determined by the phonological grammar, e.g. to a default position like a stressed syllable or domain edge. We contrast this with another type we call "targeted association", whereby the floating tone targets a numerical position , e.g. a floating H associates to the fourth TBU of the stem. Targeted association is idiosyncratic to the sponsoring morpheme, and does not necessarily target a default position. Such data have been taken as evidence for counting in grammar. Instead, we propose a novel representation we call "phantom structure", without counting. Phantom structure formalizes the observation that certain morphemes require structure to be present in order for their floating tone to be realized, but cannot provide this structure themselves. Under the targeted association type, the floating tone is pre-associated to a specific position in the phantom structure. We show that a simple grammar with two partially overlapping correspondence relations - substantive input and output structure (SubO-CORR) and phantom and output structure (PhO-CORR) - derives the association of the floating tone to the equivalent numerical position in the output as in the phantom plane input

Equilibrium pricing under relative performance concerns

We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stochastic Differential Equations (BSDE). Each agent is not only exposed to financial and non-financial risk factors, but she also faces performance concerns with respect to the other agents. Within our proposed model we prove the existence and uniqueness of an equilibrium whose analysis involves systems of fully coupled multi-dimensional quadratic BSDEs. We extend the theory of the representative agent by showing that a non-standard aggregation of risk measures is possible via weighted-dilated infimal convolution. We analyze the impact of the problem's parameters on the pricing mechanism, in particular how the agents' performance concern rates affect prices and risk perceptions. In extreme situations, we find that the concern rates destroy the equilibrium while the risk measures themselves remain stable

Chrystèle Blondeau, Un conquérant pour quatre ducs. Alexandre le Grand à la cour de Bourgogne

C’est à une bien vaste entreprise que s’est livrée Chrystèle Blondeau avec cette analyse de la figure d’Alexandre sur les différents supports iconographiques à la cour de Bourgogne. L’étude, d’une grande densité, s’avère d’autant plus ardue que tous les supports ne sont pas conservés ; ainsi en est-il des tapisseries, même si d’autres œuvres permettent de s’en faire une idée. Cette enquête conduit sur plusieurs voies, dont les différentes conclusions permettent d’affiner les conclusions de la..

Histoire de la peinture médiévale dans le royaume de Hongrie

Les études consacrées à l’art médiéval en Hongrie ont pour spécificité de traiter non seulement des monuments conservés dans ce pays, mais aussi de ceux appartenant aux espaces limitrophes qui faisaient partie du royaume de Hongrie au Moyen Âge et jusqu’à la fin de la Première Guerre mondiale. Le partage d’une partie du territoire en plusieurs états existants (Roumanie, Autriche) ou nouvellement créés (Tchécoslovaquie, Ukraine, Yougoslavie) a fait de l’art médiéval un enjeu dans l’affirmation..

Tétanos compliqué de septicémie sur hémoglobinopathie majeure

Rapporter un cas de tétanos compliqué de septicémie chez un enfant souffrant d'une hémoglobinopathie majeure. Enfant de 9 ans drépanocytaire (SC), non vacciné contre le tétanos, a été admis au CHU YO pour raideur de la nuque, difficulté à l'ouverture de la bouche et hyperthermie. L'examen à son admission notait un syndrome infectieux avec une hyperthermie (température à 39°1C), Pouls=100/mn, Fréquence cardiaque=100batt/mn, fréquence respiratoire=30cycles/mn, poids =22Kg, un trismus, une contracture des muscles para vertébraux, des paroxysmes toniques à la palpation (stade II de Mollaret), un syndrome méningé. L'examen n'avait pas retrouvé une porte d'entrée. La ponction lombaire avait ramené un liquide céphalo rachidien clair ; l'hémogramme avait montré une hyperleucocytose à 10 200/mm3, et l'hémoculture a permis d'isoler Staphylococcus aureus. Sous antibiothérapie et sous sédatifs, l'évolution a été favorable. Les porteurs d'hémoglobinopathie majeure sont plus exposés aux infections. La physiopathologie de ces infections s'explique par l'immunodépression et les troubles de la phagocytose.Un dépistage précoce de ces hémoglobinopathies, un bon suivi et une bonne couverture vaccinale des enfants drépanocytaires sont essentiels pour prévenir le tétanos et ses complications