Related papers: Explicit solution to an optimal two-player switchi…
We study a zero-sum stochastic differential switching game in infinite horizon. We prove the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities…
We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…
In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected BSDEs with interconnected barriers, we show that this game has a value and an equilibrium in the…
In this paper, we study the $m$-states optimal switching problem in finite horizon, when the switching cost functions are arbitrary and can be positive or negative. This has an economic incentive in terms of central evaluation in cases…
In this paper we consider an infinite horizon zero-sum differential game where the dynamics of each player and the running cost are also depending on the evolution of some discrete (switching) variables. In particular, such switching…
We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary ($g_{ij}(t,x)\geq 0$). We show existence of the optimal strategy, and give when…
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…
In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the…
In this paper we find viscosity solutions to the two membranes problem (that is a system with two obstacle-type equations) with two different $p-$Laplacian operators taking limits of value functions of a sequence of games. We analyze…
This paper studies the problem of the deterministic version of the Verification Theorem for the optimal m-states switching in infinite horizon under Markovian framework with arbitrary switching cost functions. The problem is formulated as…
\citeN{suzuki2020optimal} proves the uniqueness of the viscosity solution to a variational inequality which is solved by the value function of the infinite horizon optimal switching problem with simultaneous multiple switchings. Although it…
We study an optimal switching problem with a state constraint: the controller is only allowed to choose strategies that keep the controlled diffusion in a closed domain. We prove that the value function associated with this problem is the…
In this paper, we consider a differential stochastic zero-sum game in which two players intervene by adopting impulse controls in a finite time horizon. We provide a numerical solution as an approximation of the value function, which turns…
This paper introduces a new class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is governed by an infinite horizon backward…
In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming…
A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the…
In this paper we study the optimal m-states switching problem in finite horizon as well as infinite horizon with risk of default. We allow the switching cost functionals and cost of default to be of polynomial growth and arbitrary. We show…
This paper is concerned with the controller-and-stopper stochastic differential game under a regime switching model in an infinite horizon. The state of the system consists of a number of diffusions \emph{coupled} by a continuous-time…
This paper studies the problem of optimal switching for one-dimensional diffusion, which may be regarded as sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of…
In the present paper, we consider a class of two players infinite horizon differential games, with piecewise smooth costs exponentially discounted in time. Through the analysis of the value functions, we study in which cases it is possible…