Related papers: A measure-valued HJB perspective on Bayesian optim…
The objectives and contributions of this paper are mathematical and numerical analyses of a stochastic control problem of bounded population dynamics under ambiguity, an important but not well-studied problem, focusing on the optimality…
In this paper, we study a kind of optimal control problem for forward-backward stochastic differential equations (FBSDEs for short) of McKean--Vlasov type via the dynamic programming principle (DPP for short) motivated by studying the…
In this paper, a stochastic optimal control problem is investigated in which the system is governed by a stochastic functional differential equation. In the framework of functional It\^o calculus, we build the dynamic programming principle…
We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this…
Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is…
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…
The connections between optimal control and Bayesian inference have long been recognised, with the field of stochastic (optimal) control combining these frameworks for the solution of partially observable control problems. In particular,…
We introduce and study a new class of optimal switching problems, namely switching problem with controlled randomisation, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
Path Integral Control methods were developed for stochastic optimal control covering a wide class of finite horizon formulations with control affine nonlinear dynamics. Characteristic for this class is that the HJB equation is linear and…
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…
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…
This paper studies the optimal control problems of stochastic evolution equations with infinite delay of general functional type. By introducing a non-anticipative path derivative and its infinite-window dual operator, we derive the…
In this paper, we are concerned with a stochastic optimal control problem of mean-field type under partial observation, where the state equation is governed by the controlled nonlinear mean-field stochastic differential equation, moreover…
This paper is concerned with the stochastic recursive optimal control problem with mixed delay. The connection between Pontryagin's maximum principle and Bellman's dynamic programming principle is discussed. Without containing any…
In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic…
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost…
This paper considers real-time control and learning problems for finite-dimensional linear systems under binary-valued and randomly disturbed output observations. This has long been regarded as an open problem because the exact values of…
This paper derives an optimal control strategy for a simple stochastic dynamical system with constant drift and an additive control input. Motivated by the example of a physical system with an unexpected change in its dynamics, we take the…