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In this paper we study a zero-sum switching game and its verification theorems expressed in terms of either a system of Reflected Backward Stochastic Differential Equations (RBSDEs in short) with bilateral interconnected obstacles or a…

Probability · Mathematics 2020-06-30 Said Hamadène , Tingshu Mu

In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study for such a game the…

Probability · Mathematics 2014-07-29 Rainer Buckdahn , Juan Li , Marc Quincampoix

The value of a zero-sum differential games is known to exist, under Isaacs' condition, as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. In this note we provide a self-contained proof based on the construction of…

Optimization and Control · Mathematics 2013-01-29 Juan Pablo Maldonado López , Miquel Oliu-Barton

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our…

Probability · Mathematics 2011-06-15 Christine Grün

We consider a zero-sum stochastic differential game over elementary mixed feed-back strategies. These are strategies based only on the knowledge of the past state, randomized continuously in time from a sampling distribution which is kept…

Optimization and Control · Mathematics 2014-04-16 Mihai Sîrbu

In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential…

Optimization and Control · Mathematics 2023-07-12 Sheng Luo , Wenqiang Li , Xun Li , Qingmeng Wei

We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution is proved by a double penalization approach under regularity assumptions on…

Probability · Mathematics 2013-08-27 Sébastien Choukroun , Andrea Cosso , Huyen Pham

We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equation of the game turns out to be a…

Probability · Mathematics 2012-06-26 Andrea Cosso

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…

Optimization and Control · Mathematics 2016-07-21 Roxana Dumitrescu , Marie-Claire Quenez , Agnès Sulem

A zero-sum differential game with controlled jump-diffusion driven state is considered, and studied using a combination of dynamic programming and viscosity solution techniques. We prove, under certain conditions, that the value of the game…

Optimization and Control · Mathematics 2010-09-28 Imran H. Biswas

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…

Probability · Mathematics 2021-12-02 Tomasz Klimsiak , Maurycy Rzymowski

We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness. As for barriers we…

Probability · Mathematics 2018-11-01 Mateusz Topolewski

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…

Probability · Mathematics 2014-10-06 Roxana Dumitrescu , Marie-Claire Quenez , Agnès Sulem

In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limits obstacles (or barriers) when the noise is given by Brownian motion and a Poisson random measure mutually independent.…

Probability · Mathematics 2008-12-10 S. Hamadéne , H. Wang

We generalize the results of Fleming and Souganidis (1989) on zero sum stochastic differential games to the case when the controls are unbounded. We do this by proving a dynamic programming principle using a covering argument instead of…

Optimization and Control · Mathematics 2012-01-17 Erhan Bayraktar , Song Yao

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version…

Optimization and Control · Mathematics 2012-11-22 Said Hamadène , Marie-Amélie Morlais

This paper investigates two-player ergodic nonzero-sum stochastic differential games with McKean-Vlasov dynamics. We establish a verification theorem connecting solutions of coupled Hamilton-Jacobi-Bellman (HJB) Master equations to Nash…

Optimization and Control · Mathematics 2026-03-12 Qingshuo Song , Gu Wang , Zuo Quan Xu , Chao Zhu

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…

Probability · Mathematics 2025-07-09 Badr Elmansouri , Mohamed El Otmani

A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower…

Optimization and Control · Mathematics 2012-02-20 Hong Qiu , Jiongmin Yong

In this paper, we study systems of nonlinear second-order variational inequalities with interconnected bilateral obstacles with non-local terms. They are of min-max and max-min types and related to a multiple modes zero-sum switching game…

Probability · Mathematics 2017-04-06 Said Hamadene , Xuzhe Zhao