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Systems of integro-PDEs with interconnected obstacles and multi-modes switching problem driven by Lévy process

  • Said Hamadène
  • Xuxhe Zhao
Article

Abstract

In this paper we show existence and uniqueness of the solution in viscosity sense for a system of nonlinear m variational integral-partial differential equations with interconnected obstacles whose coefficients \({(f_i)_{i=1,\ldots, m}}\) depend on \({(u_j)_{j=1,\ldots,m}}\). From the probabilistic point of view, this system is related to optimal stochastic switching problem when the noise is driven by a Lévy process. The switching costs depend on (t, x). As a by-product of the main result we obtain that the value function of the switching problem is continuous and unique solution of its associated Hamilton–Jacobi–Bellman system of equations. The main tool we used is the notion of systems of reflected BSDEs with oblique reflection driven by a Lévy process.

Mathematics Subject Classification

49L25 60G40 35Q93 91G80 

Keywords

Integral-partial differential equations Interconnected obstacles Viscosity solutions Lévy process Multi-modes switching Reflected backward stochastic differential equations 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Université du Maine, LMMLe Mans Cedex 9France
  2. 2.School of Mathematics and StatisticsXidian UniversityXi’anPeople’s Republic of China

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