Related papers: Optimal control and zero-sum stochastic differenti…
A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…
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 note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic problems,…
In this work, we focus on an infinite horizon mean-field linear-quadratic stochastic control problem with jumps. Firstly, the infinite horizon linear mean-field stochastic differential equations and backward stochastic differential…
The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ The goal of the first (second) player is to…
Throughout this paper, we focused our aim on the problem of optimal control under a risk-sensitive performance functional, where the system is given by a fully coupled forward-backward stochastic differential equation with jump. The risk…
We consider a Markovian stochastic control problem with model uncertainty. The controller (intelligent player) observes only the state, and, therefore, uses feed-back (closed-loop) strategies. The adverse player (nature) who does not have a…
We study the turnpike phenomenon for optimal control problems with mean field dynamics that are obtained as the limit $N\rightarrow \infty$ of systems governed by a large number $N$ of ordinary differential equations. We show that the…
In this paper, we derive sufficient and necessary maximum principles for a stochastic optimal control problem where the system state is given by a controlled stochastic differential equation with default. We prove existence of a unique…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
This paper is concerned with a new type of differential game problems of forwardbackward stochastic systems. There are three distinguishing features: Firstly, our game systems are forward-backward doubly stochastic differential equations,…
We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…
This paper investigates a robust incentive Stackelberg stochastic differential game problem for a linear-quadratic mean field system, where the model uncertainty appears in the drift term of the leader's state equation. Moreover, both the…
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
This article discusses an optimal control problem for a phase field model of two immiscible incompressible fluid flow, incorporating surface tension effects. The optimal control problem is defined with a $L^2$-cost functional and subject to…
This paper studies a nonlinear open-loop mean field Stackelberg stochastic differential game by using the probabilistic method through the FBSDE system and the idea of taking control as the fixed point. We successively construct the…
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…
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…