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.
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Hamadène, S., Zhao, X. Systems of integro-PDEs with interconnected obstacles and multi-modes switching problem driven by Lévy process. Nonlinear Differ. Equ. Appl. 22, 1607–1660 (2015). https://doi.org/10.1007/s00030-015-0338-x
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DOI: https://doi.org/10.1007/s00030-015-0338-x