Solvability of forward-backward stochastic differential equations with nonsmooth coefficients is considered using the Four-Step Scheme and some approximation arguments. For the one-dimensional case, the existence of an adapted solution is established for the equation which allows the diffusion...

In this paper, we study a class of multi-dimensional backward stochastic differential equations (BSDEs, for short) in which the terminal values and the generators are allowed to be "discrete-functionals" of a forward diffusion. We first establish some new types of Feynman-Kac formulas related to...

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in Fuhrman et al. (2009) [12]. In other words we do not need to require the uniform exponential decay of the difference of two solutions of the underlying...

In this paper we extend the notion of "filtration-consistent nonlinear expectation" (or "-consistent nonlinear expectation") to the case when it is allowed to be dominated by a g-expectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental...

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on a terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of another diffusion which is easy for simulation, and the...

A probabilistic interpretation of a system of second order quasilinear elliptic partial differential equations under a Neumann boundary condition is obtained by introducing a kind of backward stochastic differential equations in the infinite horizon case. In the same time, a simple proof for the...

In this paper we study the integral–partial differential equations of Isaacs’ type by zero-sum two-player stochastic differential games (SDGs) with jump-diffusion. The results of Fleming and Souganidis (1989) [9] and those of Biswas (2009) [3] are extended, we investigate a controlled...

In this paper we deal with the utility maximization problem with general utility functions including power utility with liability. We derive a new approach in which we reduce the resulting control problem to the study of a system of fully-coupled Forward–Backward Stochastic Differential...

This paper concerns a class of similinear stochastic partial differential equations, of which the drift term is a second-order differential operator plus a nonlinearity, and the diffusion term is a first-order differential operator. When the nonlinearity is only continuous in the state, it is...

This paper investigates a mixed regular-singular stochastic control problem where the drift of the dynamics is quadratic in the regular control variable. More importantly, the regular control variable is constrained. The value function of the problem is derived in closed form via solving the...