Related papers: On an Ergodic Two-Sided Singular Control Problem
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which…
This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite…
This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state…
We investigate the exact enlarged controllability and optimal control of a fractional diffusion equation in Caputo sense. This is done through a new definition of enlarged controllability that allows us to extend available contributions.…
We introduce and study the basic properties of two ergodic stochastic control problems associated with the quasistationary distribution (QSD) of a diffusion process $X$ relative to a bounded domain. The two problems are in some sense dual,…
This paper studies a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching that is motivated by the optimal irreversible extraction problem of an exhaustible commodity. A company extracts a…
We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the drift is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore,…
This paper develops a quantized Q-learning algorithm for the optimal control of controlled diffusion processes on $\mathbb{R}^d$ under both discounted and ergodic (average) cost criteria. We first establish near-optimality of finite-state…
This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
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 a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
In this paper we study a Markovian two-dimensional bounded-variation stochastic control problem whose state process consists of a diffusive mean-reverting component and of a purely controlled one. The main problem's characteristic lies in…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled in…
We prove two duality descriptions of the value function for a generic stochastic optimal problem. These descriptions also hold when the diffusion is controlled, a case left open by the literature so far.
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control problems introduced in [3]. We prove that, as time horizon…