Systems of variational inequalities for non-local operators related to optimal switching problems: Existence and uniqueness

2013/06/19 by LundstrÖm, Niklas L. P., NystrÖm, Kaj, Olofsson, Marcus · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1306.4520

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.

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• On the Effectiveness of Classical Regression Methods for Optimal Switching Problems

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