Related papers: Optimal control of branching diffusion processes: …
We consider a class of exit time stochastic control problems for diffusion processes with discounted criterion, where the controller can utilize a given amount of resource, called "fuel". In contrast to the vast majority of existing…
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 study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Lipschitz continuity, semiconcavity and semiconvexity of the…
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique…
This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…
This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…
This paper introduces the formalism required to analyze a certain class of stochastic control problems that involve a super diffusion as the underlying controlled system. To establish the existence of these processes, we show that they are…
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that…
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…
In this paper, we study a stochastic optimal control problem under degenerate G-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we prove that…
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…
We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a…
We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding…
This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime switching mechanism provides the fluctuations of the random…
In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage…
We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…
Optimal control of interacting particles governed by stochastic evolution equations in Hilbert spaces is an open area of research. Such systems naturally arise in formulations where each particle is modeled by stochastic partial…
This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…
In this paper, we study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…
This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient…