Convergence of values in optimal stopping

Under the hypothesis of convergence in probability of a sequence of c\`adl\`ag processes $(X^n)_n$ to a c\`adl\`ag process $X$, we are interested in the convergence of corresponding values in optimal stopping. We give results under hypothesis of inclusion of filtrations or convergence of filtrations

Stability of solutions of BSDEs with random terminal time

In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time. More precisely, we are going to show that if $(W^n)$ is a sequence of scaled random walks or a sequence of martingales that converges to a Brownian motion $W$ and if $(\tau^n)$ is a sequence of stopping times that converges to a stopping time $\tau$, then the solution of the BSDE driven by $W^n$ with random terminal time $\tau^n$ converges to the solution of the BSDE driven by $W$ with random terminal time $\tau$.Comment: To appear in ESAIM Probability & Statistic

Convergence of values in optimal stopping and convergence of optimal stopping times

International audienceUnder the hypothesis of convergence in probability of a sequence of càdlàg processes $(X^n)_n$ to a càdlàg process $X$, we are interested in the convergence of corresponding values in optimal stopping and also in the convergence of optimal stopping times. We give results under hypothesis of inclusion of filtrations or convergence of filtrations

Novel targets and future strategies for acute cardioprotection: Position Paper of the European Society of Cardiology Working Group on Cellular Biology of the Heart

Ischaemic heart disease and the heart failure that often results, remain the leading causes of death and disability in Europe and worldwide. As such, in order to prevent heart failure and improve clinical outcomes in patients presenting with an acute ST-segment elevation myocardial infarction and patients undergoing coronary artery bypass graft surgery, novel therapies are required to protect the heart against the detrimental effects of acute ischaemia/reperfusion injury. During the last three decades, a wide variety of ischaemic conditioning strategies and pharmacological treatments have been tested in the clinic - however, their translation from experimental to clinical studies for improving patient outcomes has been both challenging and disappointing. Therefore, in this Position Paper of the European Society of Cardiology Working Group on Cellular Biology of the Heart, we critically analyse the current state of ischaemic conditioning in both the experimental and clinical settings, provide recommendations for improving its translation into the clinical setting, and highlight novel therapeutic targets and new treatment strategies for reducing acute myocardial ischaemia/reperfusion injury

Convergence de filtrations ; application à la discrétisation de processus et à la stabilité de temps d'arrêt.

This thesis deals with properties of stability of stopping problems when we don't have all the information on the model. The natural filtration of a process represent the information carried by the process along the time. Then, the properties of the sequences of natural filtrations associated to the processes are very important in this work. A first part of this study is about the stability of the notions of value in optimal stopping problem and of optimal stopping time. The first notion is the maximum value of the expectation of a function that depends on a process and on a stopping time, value taken on the set of stopping times for the natural filtration of the process. An optimal stopping time is a stopping time which realises the maximum. The second part is about the stability of the solutions of a backward stochastic differential equation with an almost surely finite terminal time when the Brownian motion that drives the equation is approximated either by a sequence of random walks, either by a sequence of martingales.Cette thèse porte sur des propriétés de stabilité de problèmes d'arrêt dans le cas où l'on dispose d'une information approximative sur le modèle. La filtration engendrée par un processus représente l'information véhiculée par ce processus au cours du temps. Aussi, les propriétés des suites de filtrations associées à des suites de processus jouent un grand rôle dans ce travail. Un premier axe d'étude concerne la stabilité des notions de réduites et de temps d'arrêt optimaux. Une réduite est la valeur maximale de l'espérance d'une fonction dépendant d'un processus et d'un temps d'arrêt, maximum pris sur l'ensemble des temps d'arrêt pour la filtration engendrée par le processus. Un temps d'arrêt optimal est un temps d'arrêt réalisant le maximum. Le second axe concerne la stabilité de solutions d'équations différentielles stochastiques rétrogrades à horizon aléatoire fini presque sûrement quand le mouvement brownien dirigeant l'équation est approché soit par une suite de marches aléatoires, soit par une suite de martingales

Corrigendum to “Stability of solutions of BSDEs with random terminal time”

This paper is a corrigendum to paper Toldo, ESAIM, P&S 10 (2006) 141–163 where we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time

Stability of solutions of BSDEs with random terminal time

In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time. More precisely, we are going to show that if (Wn) is a sequence of scaled random walks or a sequence of martingales that converges to a Brownian motion W and if $(\tau^n)$ is a sequence of stopping times that converges to a stopping time τ, then the solution of the BSDE driven by Wn with random terminal time $\tau^n$ converges to the solution of the BSDE driven by W with random terminal time τ