相关论文: Backward doubly stochastic Volterra integral equat…

In this paper,we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short) through deep learning. We first…

The paper studies the First Order BSPDEs (Backward Stochastic Partial Differential Equations) suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogs of Hamilton-Jacobi-Bellman…

In this paper, we initiate the study of backward doubly stochastic differential equations (BDSDEs, for short) with quadratic growth. The existence, comparison, and stability results for one-dimensional BDSDEs are proved when the generator…

A general and new stochastic linear quadratic optimal control problem is studied, where the coefficients are allowed to be time-varying, and both state delay and control delay can appear simultaneously in the state equation and the cost…

This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…

Connections between a system of Forward-Backward SDEs and Backward Stochastic PDEs related to the utility maximiza- tion problem is established. Besides, we derive another version of FBSDE of the same problem and prove an existence of a…

In this paper we study the class of backward doubly stochastic differential equations (BDSDEs, for short) whose terminal value depends on the history of forward diffusion. We first establish a probabilistic representation for the spatial…

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…

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…

We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…

The work of Kalman and Bucy has established a duality between filtering and optimal estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an…

The recent work by Cvitani\'c, Possama\"i, and Touzi (2018) [9] presents a general approach for continuous-time principal-agent problems, through dynamic programming and second-order backward stochastic differential equations (BSDEs). In…

This paper outlines a novel extension of the classical Pontryagin minimum (maximum) principle to stochastic optimal control problems. Contrary to the well-known stochastic Pontryagin minimum principle involving forward-backward stochastic…

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…

We deal with a new maximum principle-based stochastic control model for river management through operating a dam and reservoir system. The model is based on coupled forward-backward stochastic differential equations (FBSDEs) derived from…

In the present paper we discuss a new type of mean-field coupled forward-backward stochastic differential equations (MFFBSDEs). The novelty consists in the fact that the coefficients of both the forward as well as the backward SDEs depend…

In this paper we study, by probabilistic techniques, the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is…

This paper deals with generalized backward doubly stochastic differential equations driven by a L\'evy process (GBDSDEL, in short). Under left or right continuous and linear growth conditions, we prove the existence of minimal (resp.…

Over the last decade, a series of applied mathematics papers have explored a type of inverse problem--called by a variety of names including "inverse sensitivity", "pushforward based inference", "consistent Bayesian inference", or…