In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we investigate a new approach to the optimal stopping...

In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we investigate a new approach to the optimal stopping...

We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost functional over an infinite time-horizon through a process...

We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost functional over an infinite time-horizon through a process...

For stochastic differential equations reflecting on the boundary of a connected interval in R we discuss the problem of approximation for solutions. The main results are convergence in law as well as in Lp of discrete schemes that fundamentally generalize the classical Euler and Euler–Peano...

Constrained diffusions, with diffusion matrix scaled by small ϵ0, in a convex polyhedral cone G⊂Rk, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under...