Related papers: Verification theorem related to a zero sum stochas…
We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities…
We study a two-player nonzero-sum stochastic differential game where one player controls the state variable via additive impulses while the other player can stop the game at any time. The main goal of this work is characterize Nash…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
This paper studies a class of zero-sum stopping game in a regime switching model. A verification theorem as a sufficient criterion for Nash equilibriums is established based on a set of variational inequalities (VIs). Under an appropriate…
Control problems not admitting the dynamic programming principle are known as time-inconsistent. The game-theoretic approach is to interpret such problems as intrapersonal dynamic games and look for subgame perfect Nash equilibria. A…
In this paper, we investigate the controlled system described by forward-backward stochastic differential equations with the control contained in drift, diffusion and generator of BSDE. A new verification theorem is derived within the…
This paper is devoted to a high-dimensional mixed leadership stochastic differential game on a finite horizon in feedback information mode, where the control variables enter into the diffusion term of state equation. A verification theorem…
We consider zero-sum stochastic differential games with possibly path-dependent controlled state. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback…
This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…
In this paper we investigate two-player zero-sum stochastic differential games with an ergodic payoff, in which the diffusion coefficient does not need to be non-degenerate. We first establish the existence of a viscosity solution to the…
We show that the problem of deciding whether in a multi-player perfect information recursive game (i.e. a stochastic game with terminal rewards) there exists a stationary Nash equilibrium ensuring each player a certain payoff is Existential…
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…
In this paper, an open-loop two-person non-zero sum stochastic differential game is considered for forward-backward stochastic systems. More precisely, the controlled systems are described by a fully coupled nonlinear multi- dimensional…
In this paper, the stochastic verification theorems for stochastic control problems of reflected forward-backward stochastic differential equations are studied. We carry out the work within the frameworks of classical and viscosity…
This paper is concerned with a Stackelberg stochastic differential game on a finite horizon in feedback information pattern. A system of parabolic partial differential equations is obtained at the level of Hamiltonian to give the…
This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum…
This study investigates differential games with motion-payoff uncertainty in continuous-time settings. We propose a framework where players update their beliefs about uncertain parameters using continuous Bayesian updating. Theoretical…
We construct a saddle point in a class of zero-sum games between a stopper and a singular-controller. The underlying dynamics is a one-dimensional, time-homogeneous, singularly controlled diffusion taking values either on $\mathbb{R}$ or on…
In this paper we propose and analyze a class of $N$-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification…
We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…