Related papers: Multi-dimensional Stochastic Singular Control Via …
Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal…
We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs). We establish the…
A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang's maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the…
In this paper, we consider the optimal control problem in a 3D flow model for incompressible rigid-viscoplastic media of the Bingham kind with homogeneous Dirichlet boundary conditions and a given cost functional. On the basis of methods of…
The motivation of this paper is to prove verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term, in the case that the value function is assumed to be continuous…
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique…
A relationship between two sided discounted singular control problems and Dynkin games is established for real valued L\'evy processes. In addition, the solution of a two-sided ergodic singular control problem is obtained as the limit of…
We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state…
In this paper, we study the optimal control system driven by stochastic differential equations (SDEs) of mean-field type, in which the control variable has two components, the first being absolutely continuous and the second singular. On…
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
This paper studies {a} mixed singular/switching stochastic control problem for a multidimensional diffusion with multiples regimes on a bounded domain. Using probabilistic, partial differential equation (PDE) and penalization techniques, we…
In this work, we consider the local Cahn-Hilliard-Navier-Stokes equation with regular potential in two dimensional bounded domain. We formulate distributed optimal control problem as the minimization of a suitable cost functional subject to…
We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…
In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a…
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 mixed stochastic control problem that arises in Mathematical Finance literature with the study of interactions between dividend policy and investment. This problem combines features of both optimal switching and singular…
We consider extended mean-field control problems with multi-dimensional singular controls. A key challenge when analysing singular controls are jump costs. When controls are one-dimensional, jump costs are most naturally computed by linear…
We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field…