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This paper investigates the relationship between Pontryagin's maximum principle and dynamic programming principle in the context of stochastic optimal control systems governed by stochastic evolution equations with random coefficients in…

Optimization and Control · Mathematics 2025-11-05 Dingqian Gao , Qi Lü

This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…

Optimization and Control · Mathematics 2007-05-23 M. Papi , S. Sbaraglia

We consider stochastic dynamic programming problems with high-dimensional, discrete state-spaces and finite, discrete-time horizons that prohibit direct computation of the value function from a given Bellman equation for all states and time…

Optimization and Control · Mathematics 2020-06-05 Denis Lebedev , Paul Goulart , Kostas Margellos

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…

Robotics · Computer Science 2018-01-12 Alex A. Gorodetsky , Sertac Karaman , Youssef M. Marzouk

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 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

This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…

Optimization and Control · Mathematics 2021-11-02 Jin Won Kim , Prashant G. Mehta

In this manuscript we consider optimal control problems of stochastic differential equations with delays in the state and in the control. First, we prove an equivalent Markovian reformulation on Hilbert spaces of the state equation. Then,…

Optimization and Control · Mathematics 2024-05-20 Filippo de Feo

We study stochastic optimal control of rough stochastic differential equations (RSDEs). This is in the spirit of the pathwise control problem (Lions--Souganidis 1998, Buckdahn--Ma 2007; also Davis--Burstein 1992), with renewed interest and…

Probability · Mathematics 2025-10-24 Peter K. Friz , Khoa Lê , Huilin Zhang

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…

Optimization and Control · Mathematics 2024-07-09 Liangquan Zhang

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

The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic…

Optimization and Control · Mathematics 2014-02-06 Ioannis Tzortzis , Charalambos D. Charalambous , Themistoklis Charalambous

In this note, we study a class of indefinite stochastic McKean-Vlasov linear-quadratic (LQ in short) control problem under the control taking nonnegative values. In contrast to the conventional issue, both the classical dynamic programming…

Optimization and Control · Mathematics 2023-10-05 Xun Li , Liangquan Zhang

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

In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second…

Optimization and Control · Mathematics 2025-07-23 Jianjun Zhou , Nizar Touzi , Jianfeng Zhang

We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. In contrast with previous…

Optimization and Control · Mathematics 2012-07-17 N. V. Krylov

This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…

Portfolio Management · Quantitative Finance 2022-02-24 Christoph Belak , An Chen , Carla Mereu , Robert Stelzer

The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle…

Optimization and Control · Mathematics 2024-08-14 Bar Light

In the Dynamic Programming approach to optimal control problems a crucial role is played by the value function that is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is well known that this…

Numerical Analysis · Mathematics 2022-10-19 Luca Saluzzi , Alessandro Alla , Maurizio Falcone

This paper analyses a stochastic differential game of control and stopping in which one of the players modifies a diffusion process using impulse controls, an adversary then chooses a stopping time to end the game. The paper firstly…

Optimization and Control · Mathematics 2019-10-04 David Mguni