Related papers: Risk-sensitive Dynkin games with heterogeneous Poi…
In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…
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…
In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…
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…
We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach…
In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale…
We consider concurrent stochastic games played on graphs with reachability and safety objectives. These games can be solved by value iteration as well as strategy iteration, each of them yielding a sequence of under-approximations of the…
In this paper we study infinite horizon nonzero-sum stochastic games for controlled discrete-time Markov chains on a Polish state space with risk-sensitive ergodic cost criterion. Under suitable assumptions we show that the associated…
This paper considers a formulation of a differential game with constrained dynamics, where one player selects the dynamics and the other selects the applicable cost. When the game is considered on a finite time horizon, its value satisfies…
This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time horizon with both players adopting impulse controls. By means of BSDE methods, in…
Two-player games have had a long and fruitful history of applications stretching across the social, biological, and physical sciences. Most applications of two-player games assume synchronous decisions or moves even when the games are…
In this paper, we study a class of multi-dimensional reflected backward stochastic differential equations when the noise is driven by a Brownian motion and an independent Poisson point process, and when the solution is forced to stay in a…
We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…
We present a scheme for sequential decision making with a risk-sensitive objective and constraints in a dynamic environment. A neural network is trained as an approximator of the mapping from parameter space to space of risk and policy with…
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's…
One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The…
We address safe multi-robot interaction under uncertainty. In particular, we formulate a chance-constrained linear quadratic Gaussian game with coupling constraints and system uncertainties. We find a tractable reformulation of the game and…
This paper introduces a discrete-time stochastic game class on $\mathbb{Z}^d$, which plays the role of a toy model for the well-known problem of stochastic homogenization of Hamilton-Jacobi equations. Conditions are provided under which the…
We motivate and propose a new model for non-cooperative Markov game which considers the interactions of risk-aware players. This model characterizes the time-consistent dynamic "risk" from both stochastic state transitions (inherent to the…
The sero-sum stopping game for the stochastic sequences has been formulated in late sixties of the twenty century by Dynkin (1969). The formulation had the assumption about separability of decision moment of the players which simplified the…