Related papers: Dynamic programming principle and Hamilton-Jacobi-…

We consider a classical finite horizon optimal control problem for continuous-time pure jump Markov processes described by means of a rate transition measure depending on a control parameter and controlled by a feedback law. For this class…

This paper is concerned with the relationship between maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems. Under the smooth assumption of the value function, relations among the adjoint…

This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, the value function turns…

We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated…

The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a…

The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton-Jacobi-Bellman (HJB) equation. A…

This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence…

This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…

We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-dependent, and importantly we do not make any ellipticity…

We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding…

We study optimal control problems for interacting branching diffusion processes, a class of measure-valued dynamics capturing both spatial motion and branching mechanisms. From the perspective of the dynamic programming principle, we…

In this paper, we consider the stochastic optimal control problem for jump diffusion systems with state constraints. In general, the value function of such problems is a discontinuous viscosity solution of the Hamilton-Jacobi-Bellman (HJB)…

This paper is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity…

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…

In this paper, we consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in [10.11], we can investigate the…

In this paper we study stochastic optimal control problems of general fully coupled forward-backward stochastic differential equations (FBSDEs). In Li and Wei [8] the authors studied two cases of diffusion coefficients $\sigma$ of FSDEs, in…

We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…

We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…

We investigate a two-player zero-sum stochastic differential game problem with the state process being constrained in a connected bounded closed domain, and the cost functional described by the solution of a generalized backward stochastic…