Related papers: On controlled linear diffusions with delay in a mo…
Diffusion models have achieved remarkable success in generative modeling. Despite more stable training, the loss of diffusion models is not indicative of absolute data-fitting quality, since its optimal value is typically not zero but…
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…
Bridging the gap between diffusion models and human preferences is crucial for their integration into practical generative workflows. While optimizing downstream reward models has emerged as a promising alignment strategy, concerns arise…
This paper explores the optimal investment problem of a renewal risk model with generalized Erlang distributed interarrival times. The phases of the Erlang interarrival time is assumed to be observable. The price of the risky asset is…
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.…
This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
Diffusion models are highly effective at generating high-quality images but pose risks, such as the unintentional generation of NSFW (not safe for work) content. Although various techniques have been proposed to mitigate unwanted influences…
This paper investigates an optimal control problem where the system is described by a stochastic differential equation with extended mixed delays that contain point delay, extended distributed delay, and extended noisy memory. The model is…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
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…
This paper considers the problem of designing time-dependent, real-time control policies for controllable nonlinear diffusion processes, with the goal of obtaining maximally-informative observations about parameters of interest. More…
The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton-Jacobi-Bellman (HJB) equation. A…
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under…
This paper, which is the natural continuation of a previous paper by the same authors, studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
In this paper, a robust optimal reinsurance-investment problem with delay is studied under the $\alpha$-maxmin mean-variance criterion. The surplus process of an insurance company approximates Brownian motion with drift. The financial…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
This study considers an optimal reinsurance, investment, and dividend strategy control problem for insurance companies in a regulated Markov regime-switching environment, intending to maximize long-run average reward. Unlike existing single…