In this paper we present two general results on the existence of a discrete zero point of a function from the n-dimensional integer lattice Zn to the n-dimensional Euclidean space Rn. Under two different boundary conditions, we give a constructive proof using a combinatorial argument based on a...

We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce...

Background: Functional regions are abstract, uniformly defined territorial units that form an important basis for many development strategies of a country or a region. Objectives: This study analyses the application of network theory to the detection of such regions. Methods/Approach: Functional...