Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the uniqueness viscosity solution of the related HJBI equation

BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula

In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new type of PDE are formulated through a classical backward stochastic differential equation (BSDEs, for short) in which the terminal values and the generators are allowed to be general functions of Brownian paths. In this way we have established a new type of nonlinear Feynman-Kac formula for a general non-Markovian BSDE. Some main properties of regularities for this new PDE was obtained

Multi-dimensional BSDEs with mean reflection

In this paper, we consider multi-dimensional mean reflected backward stochastic differential equations (BSDEs) with possibly non-convex reflection domains along inward normal direction, which were introduced by Briand, Elie and Hu [6] in the scalar case. We first apply a fixed-point argument to establish the uniqueness and existence result under an additional bounded condition on the driver. Then, with the help of a priori estimates, we develop a successive approximation procedure to remove the additional bounded condition for the general case

General Mean Reflected BSDEs

The present paper is devoted to the study of backward stochastic differential equations with mean reflection formulated by Briand et al. [7]. We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on the distribution of the solution term $Y$. Using a fixed-point argument, BMO martingale theory and the $\theta$-method, we establish the existence and uniqueness result for such BSDEs in several typical situations, including the case where the driver is quadratic with bounded or unbounded terminal condition.Comment: 20 page