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

@article{Hamadne2014SystemsOI,
  title={Systems of integro-PDEs with interconnected obstacles and multi-modes switching problem driven by L{\'e}vy process},
  author={Said Hamad{\`e}ne and Xuxhe Zhao},
  journal={Nonlinear Differential Equations and Applications NoDEA},
  year={2014},
  volume={22},
  pages={1607-1660}
}
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 $${(f_i)_{i=1,\ldots, m}}$$(fi)i=1,…,m depend on $${(u_j)_{j=1,\ldots,m}}$$(uj)j=1,…,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… CONTINUE READING
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