Related papers: Probabilistic Interpretation for Systems of Isaacs…

In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined via generalized backward stochastic differential equations…

The aim of this short note is to fill in a gap in our earlier paper [16] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [15]. We also provide more insight on the properties of 2RBSDEs,…

In this paper, we study a multi-dimensional backward stochastic differential equation (BSDE) with oblique reflection, which is a BSDE reflected on the boundary of a special unbounded convex domain along an oblique direction, and which…

We formulate a new class of two-person zero-sum differential games, in a stochastic setting, where a specification on a target terminal state distribution is imposed on the players. We address such added specification by introducing…

We study the problem of existence of solutions for generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under weaker assumptions on the data. Roughly speaking we show the existence of a…

In this paper, we investigate the well-posedness of bounded and unbounded solutions for reflected backward stochastic differential equations (RBSDEs) and backward stochastic differential equations (BSDEs). The generators of these equations…

A key challenge in multi-agent systems is the design of intelligent agents solving real-world tasks in close interaction with other agents (e.g. humans), thereby being confronted with a variety of behavioral variations and limited knowledge…

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…

In the theory of games on infinite-state arenas, there is a stark contrast between (i) recursion-based models such as pushdown systems and extensions on one hand, and (ii) counter-based models like vector addition systems with states (VASS)…

In this paper{\}we prove the existence of a solution for reflected backward doubly stochastic differential equations with poisson jumps (RBDSDEPs) with one continuous barrier where the generator is continuous and also we study the RBDSDEPs…

We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where…

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…

In this paper we prove an approximation result for the viscosity solution of a system of semi-linear partial differential equations with continuous coefficients and nonlinear Neumann boundary condition. The approximation we use is based on…

This paper studies discrete-time two-person nonzero-sum linear quadratic stochastic games with random coefficients. Using convex variational analysis, we derive necessary and sufficient conditions for the existence of open-loop Nash…

This paper studies a system of $m$ variational inequalities with interconnected obstacles in infinite horizon associated to optimal multi-modes switching problems. Our main result is the existence and uniqueness of a continuous solution in…

In stochastic games with incomplete information, the uncertainty is evoked by the lack of knowledge about a player's own and the other players' types, i.e. the utility function and the policy space, and also the inherent stochasticity of…

This paper is devoted to a stochastic differential game of functional forward-backward stochastic differential equation (FBSDE, for short). The associated upper and lower value functions of the stochastic differential game are defined by…

We address the problem of mechanism design for two-stage repeated stochastic games -- a novel setting using which many emerging problems in next-generation electricity markets can be readily modeled. Repeated playing affords the players a…

This paper provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and…

In the present paper, we study a two-player zero-sum deterministic differential game with both players adopting impulse controls, in infinite time horizon, under rather weak assumptions on the cost functions. We prove by means of the…