English
Related papers

Related papers: Stochastic control with rough paths

200 papers

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…

Probability · Mathematics 2008-12-20 Seid Bahlali

We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…

Optimization and Control · Mathematics 2022-11-17 Yumiharu Nakano

In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost…

Optimization and Control · Mathematics 2022-06-28 Mingshang Hu , Shaolin Ji , Xiaojuan Li

We study the small time path behavior of double stochastic integrals of the form $\int_0^t(\int_0^rb(u) dW(u))^T dW(r)$, where $W$ is a $d$-dimensional Brownian motion and $b$ is an integrable progressively measurable stochastic process…

Probability · Mathematics 2007-05-23 Patrick Cheridito , H. Mete Soner , Nizar Touzi

This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…

Optimization and Control · Mathematics 2014-08-26 Jingtao Shi , Huanshui Zhang

We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The…

We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…

Probability · Mathematics 2017-02-17 Francesco Cordoni , Luca Di Persio

Density function describes the density of states in the state space of a dynamic system or a Markov Decision Process (MDP). Its evolution follows the Liouville equation. We show that the density function is the dual of the value function in…

Systems and Control · Computer Science 2019-11-11 Yuxiao Chen , Aaron D. Ames

A robust control problem is considered in this paper, where the controlled stochastic differential equations (SDEs) include ambiguity parameters and their coefficients satisfy non-Lipschitz continuous and non-linear growth conditions, the…

Mathematical Finance · Quantitative Finance 2022-08-24 Zhou Yang , Jing Zhang , Chao Zhou

In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general…

Probability · Mathematics 2008-04-04 Rainer Buckdahn , Jin Ma , Catherine Rainer

In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…

Optimization and Control · Mathematics 2018-09-07 AbdulRahman Al-Hussein , Boulakhras Gherbal

In this paper, we study a stochastic optimal control problem under a type of consistent convex expectation dominated by G-expectation. By the separation theorem for convex sets, we get the representation theorems for this convex expectation…

Optimization and Control · Mathematics 2024-08-21 Xiaojuan Li , Mingshang Hu

The purpose of this article is to study a stochastic control problem on a junction, with control at the junction point. The problem of control is formulated in the weak sense, using a relaxed control, namely a control which takes values in…

Optimization and Control · Mathematics 2023-11-28 Isaac Ohavi

In this paper we develop necessary conditions for optimality, in the form of the Pontryagin maximum principle, for the optimal control problem of a class of infinite dimensional evolution equations with delay in the state. In the cost…

Probability · Mathematics 2017-06-12 Giuseppina Guatteri , Federica Masiero , Carlo Orrieri

This note lays part of the theoretical ground for a definition of differential systems modeling reinforcement learning in continuous time non-Markovian rough environments. Specifically we focus on optimal relaxed control of rough equations…

Optimization and Control · Mathematics 2024-02-29 Prakash Chakraborty , Harsha Honnappa , Samy Tindel

In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for…

Probability · Mathematics 2020-08-13 Yunhong Li , Anis. Matoussi , Lifeng Wei , Zhen Wu

We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2. We apply an anticipative Girsanov transformation to transform the system into another one, driven only by…

Optimization and Control · Mathematics 2016-05-06 Rainer Buckdahn , Shuai Jing

This work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve…

Systems and Control · Electrical Eng. & Systems 2023-07-26 Maico Hendrikus Wilhelmus Engelaar , Sofie Haesaert , Mircea Lazar

We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…

Optimization and Control · Mathematics 2025-08-08 Anderson O. Calixto , Bernardo Freitas Paulo da Costa , Glauco Valle

This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the…

Optimization and Control · Mathematics 2016-08-02 Qingshuo Song , Chao Zhu