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We analyze a stochastic optimal control problem, where the state process follows a McKean-Vlasov dynamics and the diffusion coefficient can be degenerate. We prove that its value function V admits a nonlinear Feynman-Kac representation in…

Probability · Mathematics 2016-11-15 Erhan Bayraktar , Andrea Cosso , Huyên Pham

The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…

Probability · Mathematics 2013-03-26 René Carmona , Francois Delarue

We study an optimal control problem of McKean--Vlasov branching diffusion processes, in which the interaction term is determined by the marginal measure induced by all alive particles in the system. Accordingly, the value function is…

Optimization and Control · Mathematics 2025-12-02 Julien Claisse , Jiazhi Kang , Tianxu Lan , Xiaolu Tan

This paper is devoted to a viscosity solution theory of the stochastic Hamilton-Jacobi-Bellman equation in the Wasserstein spaces for the mean-field type control problem which allows for random coefficients and may thus be non-Markovian.…

Optimization and Control · Mathematics 2023-10-24 Hang Cheung , Jinniao Qiu , Alexandru Badescu

In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…

Probability · Mathematics 2020-09-15 Qian Lin

We study the optimal control of path-dependent McKean-Vlasov equations valued in Hilbert spaces motivated by non Markovian mean-field models driven by stochastic PDEs. We first establish the well-posedness of the state equation, and then we…

Optimization and Control · Mathematics 2022-12-21 Andrea Cosso , Fausto Gozzi , Idris Kharroubi , Huyên Pham , Mauro Rosestolato

We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is…

Probability · Mathematics 2016-09-12 Elena Bandini , Andrea Cosso , Marco Fuhrman , Huyên Pham

We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…

Optimization and Control · Mathematics 2024-07-19 M. Soledad Aronna , Michele Palladino , Oscar Sierra

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…

Optimization and Control · Mathematics 2021-09-17 Kaito Ito , Takuya Ikeda , Kenji Kashima

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

This paper aims to explore the relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients. Under certain regular conditions for the coefficients, the…

Optimization and Control · Mathematics 2020-12-10 Yuchao Dong , Qingxin Meng , Qi Zhang

We investigate an optimal control problem motivated by neuroscience, where the dynamics is driven by a Poisson process with a controlled stochastic intensity and an unknown parameter. Given a prior distribution for the unknown parameter, we…

Optimization and Control · Mathematics 2025-12-23 Nicolas Baradel , Quentin Cormier

We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…

Probability · Mathematics 2016-03-15 Rainer Buckdahn , Tianyang Nie

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…

Optimization and Control · Mathematics 2013-01-03 Shaolin Ji , Shuzhen Yang

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…

Probability · Mathematics 2017-03-09 Huyên Pham

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 system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…

Probability · Mathematics 2013-01-03 Shaolin Ji , Shuzhen Yang

We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value function is the unique Crandall-Lions viscosity solution of the…

Probability · Mathematics 2023-08-04 Andrea Cosso , Fausto Gozzi , Mauro Rosestolato , Francesco Russo

We investigate the complexities of the McKean-Vlasov optimal control problem, exploring its various formulations such as the strong and weak formulations, as well as both Markovian and non-Markovian setups within financial markets.…

Optimization and Control · Mathematics 2024-04-29 Timothy Bennett

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