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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…

In this paper, we study the optimal singular controls for stochastic recursive systems, in which the control has two components: the regular control, and the singular control. Under certain assumptions, we establish the dynamic programming…

We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated…

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…

We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…

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 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 investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…

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…

We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…

In this paper we study the fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equation for the optimal stochastic control problem of stochastic differential equations with random coefficients. The notion of viscosity solution is…

We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…

In this paper, we explore a new class of stochastic control problems characterized by specific control constraints. Specifically, the admissible controls are subject to the ratcheting constraint, meaning they must be non-decreasing over…

This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…

This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness…

Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is…

We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for…

We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that a multidimensional Markovian stochastic factor drives both of them. Moreover, we model…

This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…

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…