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This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime switching mechanism provides the fluctuations of the random…
The paper deals with a zero-sum differential game for a dynamical system which motion is described by a nonlinear delay differential equation under an initial condition defined by a piecewise continuous function. The corresponding Cauchy…
We introduce a method for approximating viscosity solutions of stationary degenerate elliptic Hamilton--Jacobi--Bellman equations on bounded domains arising in stochastic exit-time control. Viscosity enforcement is formulated as a min--max…
In this paper, we study initial-boundary value problems for the Cahn--Hilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding…
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…
We study the smoothness of the upper and lower value functions of stochastic differential games in the framework of time-homogeneous (possibly degenerate) diffusion processes in a domain, under the assumption that the diffusion, drift and…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that…
In this paper, we consider state and control path-dependent stochastic zero-sum differential games, where the dynamics and the running cost include both state and control paths of the players. Using the notion of nonanticipative strategies,…
In this manuscript we consider optimal control problems of stochastic differential equations with delays in the state and in the control. First, we prove an equivalent Markovian reformulation on Hilbert spaces of the state equation. Then,…
We study a finite-horizon differential game of pursuit-evasion like, between a single player and a mass of agents. The player and the mass directly control their own evolution, which for the mass is given by a first order PDE of transport…
We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this…
We consider impulse control of stochastic functional differential equations (SFDEs) driven by L\'evy processes under an additional $L^p$-Lipschitz condition on the coefficients. Our results, which are first derived for a general stochastic…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
In this paper we deal with infinite horizon optimal control problems. Basing on weak variations in an extremal problem in weighted function spaces we prove necessary conditions in form of the adjoint equation and a variational inequality.…
The paper is concerned with a kind of minimal time control problem for the heat equation with impulse controls. The purpose of such a problem is to find an optimal impulse control (among certain control constraint set) steering the solution…
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the…
Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant $\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the reflections…
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 one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential…