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...

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 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...

A coupled forward–backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier–Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the Reynolds number is small or the dimension of the...

This article presents new results on the problem of selecting (online) a monotone subsequence of maximum expected length from a sequence of i.i.d. random variables. We study the case where the variables are observed sequentially at the occurrence times of a Poisson process with known rate. Our...