相关论文: Games of singular control and stopping driven by s…

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…

We consider a stochastic differential equation that is controlled by means of an additive finite-variation process. A singular stochastic controller, who is a minimizer, determines this finite-variation process, while a discretionary…

We consider a class of zero-sum stopper vs. singular-controller games in which the controller can only act on a subset $d_0<d$ of the $d$ coordinates of a controlled diffusion. Due to the constraint on the control directions these games…

We consider a zero-sum stochastic game for continuous-time Markov chain with countable state space and unbounded transition and pay-off rates. The additional feature of the game is that the controllers together with taking actions are also…

We study a class of zero-sum games between a singular-controller and a stopper over finite-time horizon. The underlying process is a multi-dimensional (locally non-degenerate) controlled stochastic differential equation (SDE) evolving in an…

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…

We consider a class of two-sided singular control problems. A controller either increases or decreases a given spectrally negative Levy process so as to minimize the total costs comprising of the running and control costs where the latter…

The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates, while only one player can choose a stopping time. We use the dynamic programming…

Following Baurdoux and Kyprianou [2] we consider the McKean stochastic game, a game version of the McKean optimal stopping problem (American put), driven by a spectrally negative Levy process. We improve their characterisation of a saddle…

We study a class of zero-sum stochastic games between a stopper and a singular-controller, previously considered in [Bovo and De Angelis (2025)]. The underlying singularly-controlled dynamics takes values in…

We study zero-sum stochastic games between a singular controller and a stopper when the (state-dependent) diffusion matrix of the underlying controlled diffusion process is degenerate. In particular, we show the existence of a value for the…

In this note, we study a class of stochastic control problems where the optimal strategies are described by two parameters. These include a subset of singular control, impulse control, and two-player stochastic games. The parameters are…

We prove existence of a value for two-player zero-sum stopper vs. singular-controller games on finite-time horizon, when the underlying dynamics is one-dimensional, diffusive and bound to evolve in $[0,\infty)$. We show that the value is…

In a probabilistic mean field game driven by a L\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\`adl\`ag processes, while he is…

Zero sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics , we completely characterize…

This paper studies game-type credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default…

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,…

The purpose of this paper is to study 2-person zero-sum stochastic differential games, in which one player is a major one and the other player is a group of $N$ minor agents which are collectively playing, statistically identical and have…

Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…

Zero-sum mean payoff games can be studied by means of a nonlinear spectral problem. When the state space is finite, the latter consists in finding an eigenpair $(u,\lambda)$ solution of $T(u)=\lambda \mathbf{1} + u$ where $T:\mathbb{R}^n…