Related papers: A measure-valued HJB perspective on Bayesian optim…
This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
We consider a general class of stochastic optimal control problems, where the state process lives in a real separable Hilbert space and is driven by a cylindrical Brownian motion and a Poisson random measure; no special structure is imposed…
Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior…
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…
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic…
This paper is concerned with optimal control problems for systems governed by mean-field stochastic differential equation, in which the control enters both the drift and the diffusion coefficient. We prove that the relaxed state process,…
The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…
We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the It\^o-Ventzell formula the system is transformed to a controlled backward stochastic…
This paper studies a robust stochastic control problem with a monotone mean-variance cost functional and random coefficients. The main technique is to find the saddle point through two backward stochastic differential equations (BSDEs) with…
This paper provides a unifying theoretical framework for stochastic optimization algorithms by means of a latent stochastic variational problem. Using techniques from stochastic control, the solution to the variational problem is shown to…
A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. A novel Bayesian theory is developed for detecting a…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
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…
This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and…
This work addresses a switching control problem under which the cost associated with the changes of regimes is allowed to have discontinuities in time. Our main contribution is to show several characterizations of the optimal cost function…
This paper studies stochastic control problems motivated by optimal consumption with wealth benchmark tracking. The benchmark process is modeled by a combination of a geometric Brownian motion and a running maximum process, indicating its…
Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton-Jacobi-Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the…
Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on…