Related papers: Mokobodzki's intervals: an approach to Dynkin game…
We study reflected backward stochastic differential equation (RBSDEs) on the probability space equipped with a Brownian motion. The main novelty of the paper lies in fact that we consider the following weak assumptions on the data: barriers…
We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ do not satisfy any regularity assumption and with a general filtration. Under a technical assumption (a Mokobodzki-type condition), we show…
We consider reflected backward stochastic differential equations with two optional barriers of class (D) satisfying Mokobodzki's separation condition and coefficient which is only continuous and non-increasing. We assume that data are…
We introduce a generalized Dynkin game problem with non linear conditional expectation ${\cal E}$ induced by a Backward Stochastic Differential Equation (BSDE) with jumps. Let $\xi, \zeta$ be two RCLL adapted processes with $\xi \leq…
We revisit the Dynkin game problem in a general framework, improve classical results and relax some assumptions. The criterion is expressed in terms of families of random variables indexed by stopping times. We construct two nonnegative…
In this paper, we study the doubly conditional reflected backward stochastic differential equations (BSDEs), where constraints are made on the conditional expectation of the first component of the solution with respect to a general…
We introduce a new class of reflected backward stochastic differential equations with two c\`adl\`ag barriers, which need not satisfy any separation conditions. For that reason, in general, the solutions are not semimartingales. We prove…
We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general \cadlag measurable processes. As a by-product of…
In this paper, we want to investigate some kind of Dynkin's game under ambiguity which is represented by Backward Stochastic Differential Equation (shortly BSDE) with standard generator function g(t, y, z). Under regular assumptions, a pair…
We formulate a notion of doubly reflected BSDEs with a default time and two completely separated RCLL barriers. We demonstrate the existence and uniqueness of the solution. Within the defaultable setup, we introduce a type of generalized…
We introduce a mixed {\em generalized} Dynkin game/stochastic control with ${\cal E}^f$-expectation in a Markovian framework. We study both the case when the terminal reward function is supposed to be Borelian only and when it is…
In this paper we introduce a new type of norms for semimartingales, under both linear and nonlinear expectations. Our norm is defined in the spirit of quasimartingales, and it characterizes square integrable semimartingales. This work is…
The aim of this paper is twofold. First, we extend the results of [33] concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar…
Zero-sum Dynkin games under Poisson constraints, where players can only stop at the event times of a Poisson process, have been studied widely in the recent literature. The constraint can be modelled in two ways: either both players share…
A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang's maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the…
In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous,…
This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and…
We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum…
In this paper, we analyze mean-field game modulated by finite states markov chains. We first develop a sufficient stochastic maximum principle for the optimal control of a Markov-modulated stochastic differential equation (SDE) of…
We construct an aggregated version of the value processes associated with stochastic control problems, where the criterion to optimise is given by solutions to semi-martingale backward stochastic differential equations (BSDEs). The results…