Related papers: On the optimally controlled stochastic shallow lak…
We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent…
In optimal control problems defined on stratified domains, the dynamics and the running cost may have discontinuities on a finite union of submanifolds of RN. In [8, 5], the corresponding value function is characterized as the unique…
We study the welfare function of the deterministic and stochastic shallow lake problem. We show that the welfare function is the viscosity solution of the associated Bellman equation, we establish several properties including its asymptotic…
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…
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…
This paper explores the application of nonsmooth analysis in the Wasserstein space to finite-horizon optimal control problems for nonlocal continuity equations. We characterize the value function as a strict viscosity solution of the…
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…
We consider the optimal control problem associated with a general version of the well known shallow lake model, and we prove the existence of an optimum in the class $L_{loc}^{1}\left(0,+\infty\right)$. Any direct proof seems to be missing…
We present a modern stochastic control framework for dynamic optimization of river environment and ecology. We focus on a fisheries problem in Japan, and show several examples of simplified optimal control problems of stochastic…
We consider a Bayesian adaptive optimal stochastic control problem where a hidden static signal has a non-separable influence on the drift of a noisy observation. Being allowed to control the specific form of this dependence, we aim at…
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…
This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime-switching is introduced. The decision-makers either harvest or renew with finite…
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…
We study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Lipschitz continuity, semiconcavity and semiconvexity of the…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space.…
In this paper, we investigate stochastic versions of the Hopf-Lax formula which are based on compositions of the Hopf-Lax operator with the transition kernel of a L\'evy process taking values in a separable Banach space. We show that,…
We study the stochastic control-stopping problem when the data are of polynomial growth. The approach is based on backward stochastic dierential equations (BSDEs for short). The problem turns into the study of a specic reected BSDE with a…
We prove the continuity of the value function of the sparse optimal control problem. The sparse optimal control is a control whose support is minimum among all admissible controls. Under the normality assumption, it is known that a sparse…