Related papers: Optimal control of branching diffusion processes: …
In this paper we consider the optimal control of Hilbert space-valued infinite-dimensional Piecewise Deterministic Markov Processes (PDMP) and we prove that the corresponding value function can be represented via a Feynman-Kac type formula…
We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…
When randomness in demand affects the sales of a product, retailers use dynamic pricing strategies to maximize their profits. In this article, we formulate the pricing problem as a continuous-time stochastic optimal control problem and find…
We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…
This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and…
In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent…
In this paper, we consider the stochastic optimal control problem for jump diffusion systems with state constraints. In general, the value function of such problems is a discontinuous viscosity solution of the Hamilton-Jacobi-Bellman (HJB)…
This work concerns the optimal control problem for McKean-Vlasov SDEs. We provide explicit conditions to ensure the existence of optimal Markovian feedback controls. Moreover, based on the flow property of the McKean-Vlasov SDE, the dynamic…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
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…
This paper analyzes a discretization of a stochastic parabolic optimal control problem, where the diffusion term contains the control variable. With rough data, the convergence of the discretization is derived. In addition, a Monte-Carlo…
In this work we study the stochastic recursive control problem, in which the aggregator (or called generator) of the backward stochastic differential equation describing the running cost is continuous but not necessarily Lipschitz with…
The paper considers the optimal control problem of inventory of a discrete product in regeneration scheme with a Poisson flow of customer requirements. In the system deferred demand is allowed, the volume of which is limited by a given…
We address a long-standing open problem in risk theory, namely the optimal strategy to pay out dividends from an insurance surplus process, if the dividend rate can never be decreased. The optimality criterion here is to maximize the…
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…
We study optimal control problems in infinite horizon when the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (inspired by traffic models). We adapt the results in [H. M.…
We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential…
We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely…
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…
This contribution mainly focuses on the finite horizon optimal control problems of a susceptible-infected-vaccinated(SIV) epidemic system governed by reaction-diffusion equations and Markov switching. Stochastic dynamic programming is…