Systems of Integro-PDEs with Interconnected Obstacles and Multi-Modes Switching Problem Driven by L��vy Process
| Autor: | Hamad��ne, Sa��d, Zhao, Xuzhe |
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| Rok vydání: | 2014 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1408.2759 |
| Popis: | 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 $(f_i)_{i=1,\cdots, m}$ depend on $(u_j)_{j=1,\cdots,m}$. From the probabilistic point of view, this system is related to optimal stochastic switching problem when the noise is driven by a L��vy 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 L��vy process. 41 pages |
| Databáze: | OpenAIRE |
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