Related papers: Stochastic control with rough paths
In this paper, we explore a new class of stochastic control problems characterized by specific control constraints. Specifically, the admissible controls are subject to the ratcheting constraint, meaning they must be non-decreasing over…
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…
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…
This paper studies {a} mixed singular/switching stochastic control problem for a multidimensional diffusion with multiples regimes on a bounded domain. Using probabilistic, partial differential equation (PDE) and penalization techniques, we…
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 derive an algorithm in the spirit of Rogers and Davis & Burstein that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recently obtained in the work of Guyon & Henry-Labord\`ere. We…
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…
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 proposes to parameterize open loop controls in stochastic optimal control problems via suitable classes of functionals depending on the driver's path signature, a concept adopted from rough path integration theory. We rigorously…
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…
We consider a two-sided singular stochastic control problem with a risk-sensitive ergodic criterion. In particular, we consider a stochastic system whose uncontrolled dynamics are modelled by a linear diffusion. The control that can be…
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…
We consider a class of discrete time stochastic control problems motivated by some financial applications. We use a pathwise stochastic control approach to provide a dual formulation of the problem. This enables us to develop a numerical…
This paper deals with a family of stochastic control problems in Hilbert spaces which arises in typical applications (such as boundary control and control of delay equations with delay in the control) and for which is difficult to apply the…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
In this note, we consider an optimal control problem associated to a differential equation driven by a H\"{o}lder continuous function g of index greater than 1/2. We split our study in two cases. If the coefficient of dg\_t does not depend…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
This paper is about operator-theoretic methods for solving nonlinear stochastic optimal control problems to global optimality. These methods leverage on the convex duality between optimally controlled diffusion processes and…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…