Q. S. Song | Searcharxiv

arXiv2006

Existence of Saddle Points in Discrete Markov Games and Its Application in Numerical Methods for Stochastic Differential Games

This work establishes sufficient conditions for existence of saddle points in discrete Markov games. The result reveals the relation between dynamic games and static games using dynamic programming equations. This result enables us to prove existence of saddle points of non-separable stochastic differential games of regime-switching diffusions under appropriate conditions.

math.OC↗

arXiv2006

An Epsilon-uniform Finite Element Method for Singularly Perturbed Boundary Value Problems

This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new finite element solution always intersect with original one at fixed point. Using this fact, an effective epsilon-uniform approximation out of boundary is proposed by adding one point only in the grid that contains boundary layer. The thickness of boundary layer is not necessary to be known from priori estimation. Numerical results are carried out and compared to Shishkin mesh for demonstration purpose.

math.NA↗