English
Related papers

Related papers: Stochastic control with rough paths

200 papers

We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…

Probability · Mathematics 2014-11-17 I. Bailleul , J. Diehl

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…

Optimization and Control · Mathematics 2021-03-08 Tom Lefebvre , Guillaume Crevecoeur

A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…

Optimization and Control · Mathematics 2017-05-03 Shinji Tanimoto

In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…

Optimization and Control · Mathematics 2023-02-20 Filippo de Feo , Salvatore Federico , Andrzej Święch

This paper analyzes a discretization of a stochastic parabolic optimal control problem, where the diffusion term contains the control variable. With rough data, the convergence of the discretization is derived. In addition, a Monte-Carlo…

Numerical Analysis · Mathematics 2022-08-31 Binjie Li , Qin Zhou , Xiaoping Xie

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…

Optimization and Control · Mathematics 2026-03-27 Jingwei Chen , Jun Ye , Feng Chen

In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be…

Optimization and Control · Mathematics 2019-05-02 Liangquan Zhang , Xun Li

In this paper we study the fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equation for the optimal stochastic control problem of stochastic differential equations with random coefficients. The notion of viscosity solution is…

Optimization and Control · Mathematics 2018-07-16 Jinniao Qiu

A general continuous mean-variance problem is considered for a diffusion controlled process where the reward functional has an integral and a terminal-time component. The problem is transformed into a superposition of a static and a dynamic…

Probability · Mathematics 2019-05-16 Georgios Aivaliotis , Alexander Yu. Veretennikov

In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…

Optimization and Control · Mathematics 2013-06-07 Mingshang Hu , Shaolin Ji , Shuzhen Yang

We present a new version of the stochastic sewing lemma, capable of handling multiple discontinuous control functions. This is then used to develop a theory of rough stochastic analysis in a c\`adl\`ag setting. In particular, we define…

Probability · Mathematics 2026-03-30 Andrew L. Allan , Jost Pieper

This paper investigates a multidimensional non-homogeneous stochastic linear-quadratic optimal control problem featuring random coefficients and a terminal mean-field term in the cost functional, enabling its direct application to…

Optimization and Control · Mathematics 2026-05-27 Guojiang Shao , Zuo Quan Xu , Qi Zhang

We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is…

Optimization and Control · Mathematics 2010-08-31 Mohamed Mnif

In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path,…

Probability · Mathematics 2025-04-28 Yuzuru Inahama

We study controlled differential equations with unbounded drift terms, where the driving paths is $\nu$ - H\"older continuous for $\nu \in (\frac{1}{3},\frac{1}{2})$, so that the rough integral are interpreted in the Gubinelli sense…

Probability · Mathematics 2020-10-19 Luu Hoang Duc

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…

Mathematical Finance · Quantitative Finance 2026-01-08 Chonghu Guan , Jiacheng Fan , Zuo Quan Xu

Standard stochastic control methods assume that the probability distribution of uncertain variables is available. Unfortunately, in practice, obtaining accurate distribution information is a challenging task. To resolve this issue, we…

Optimization and Control · Mathematics 2021-10-13 Insoon Yang

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…

Optimization and Control · Mathematics 2014-10-15 Mingshang Hu , Shaolin Ji

Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…

Statistics Theory · Mathematics 2024-05-28 Sören Christensen , Claudia Strauch , Lukas Trottner

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…

Probability · Mathematics 2021-09-21 Côme Huré , Huyên Pham , Achref Bachouch , Nicolas Langrené