Related papers: Optimal control of diffusion processes pertaining …
In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…
A heroin epidemic mathematical model with prevention information and treatment, as control interventions, is analyzed, assuming that an individual's behavioral response depends on the spreading of information about the effects of heroin.…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
We present an analytic solution of a differential-difference equation that appears when one solves an optimal stopping time problem with state process following a jump-diffusion process. This equation occurs in the context of real options…
We study a time-optimal control problem of a two-peakon collision. First, we state the controllability. Next, we find the time-optimal strategy. This is done via the HamiltonJacobi-Bellman equation and the dynamic programming method. We…
In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching…
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…
Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…
This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are…
We study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at jump times of independent Poisson process. Under relatively weak…
In the last few years there has been renewed interest in the classical control problem of de Finetti for the case that underlying source of randomness is a spectrally negative Levy process. In particular a significant step forward is made…
The paper concerns the infinite dimensional Hamilton-Jacobi-Bellman equation related to optimal control problem regulated by a transport equation with boundary control. A suitable viscosity solution approach is needed in view of the…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
We study a class of singular stochastic control problems for a one-dimensional diffusion $X$ in which the performance criterion to be optimised depends explicitly on the running infimum $I$ (or supremum $S$) of the controlled process. We…
The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like…
We consider the problem of minimizing the asymptotic exit rate with which the controlled-diffusion process of a stochastically perturbed multi-channel dynamical system exits from a given bounded open domain. In particular, for a class of…
This paper introduces a new type of second order stochastic backward Hamilton-Jacobi-Bellman (HJB) equations for optimal stochastic control problems with a currently observable but non-predicable parameter process, in addition to 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…
In this paper we propose and analyze a method based on the Riccati transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation arising from the stochastic dynamic optimal allocation problem. We show how the fully nonlinear…