Systems of variational inequalities for non-local operators related to optimal switching problems: Existence and uniqueness
Abstract
In this paper we study a system of variational inequalities where the operator is non-local, possibly degenerate and of second order. A special case of this type of problem occurs in the context of optimal switching problems when the dynamics of the underlying state variables is described by an N-dimensional Levy process. We establish a general comparison principle for viscosity sub- and supersolutions to the system under mild regularity, growth and structural assumptions on the data. Using the comparison principle we then prove the existence of a unique viscosity solution to the system by Perron's method. Our main contribution is that we establish existence and uniqueness of viscosity solutions, in the setting of Levy processes and non-local operators, with no sign assumption on the switching costs and allowing them to depend on x as well as t.
Keywords
Cite
@article{arxiv.1306.4520,
title = {Systems of variational inequalities for non-local operators related to optimal switching problems: Existence and uniqueness},
author = {Niklas L. P. LundstrÖm and Kaj NystrÖm and Marcus Olofsson},
journal= {arXiv preprint arXiv:1306.4520},
year = {2013}
}