Related papers: Time-inconsistent singular control problems: Refle…
We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
In this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational…
This paper is devoted to studying an infinite time horizon stochastic recursive control problem with jumps, where infinite time horizon stochastic differential equation and backward stochastic differential equation with jumps describe the…
We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a probabilistic approach…
This paper is devoted to solving a time-inconsistent risk-sensitive control problem with parameter $\e$ and its limit case ($\e\rightarrow0^+$) for countable-stated Markov decision processes (MDPs for short). Since the cost functional is…
For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…
This paper deals with a stochastic optimal feedback control problem for the controlled stochastic partial differential equations. More precisely, we establish the existence of stochastic optimal feedback control for the controlled…
As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…
This work theoretically studies a ubiquitous reinforcement learning policy for controlling the canonical model of continuous-time stochastic linear-quadratic systems. We show that randomized certainty equivalent policy addresses the…
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 the present paper, we study the existence and optimal controllability of a multi-term time-fractional stochastic system with non-instantaneous impulses. Using semigroup theory, stochastic analysis theory, and Krasnoselskii's fixed point…
We consider optimal control problems for diffusion processes, where the objective functional is defined by a time-consistent dynamic risk measure. We focus on coherent risk measures defined by $g$-evaluations. For such problems, we…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…
This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…
This paper characterizes differentiable and subgame Markov perfect equilibria in a continuous time intertemporal decision problem with non-constant discounting. Capturing the idea of non commitment by letting the commitment period being…