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Applied Mathematics and Optimization

, Volume 62, Issue 1, pp 47–80 | Cite as

Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes

  • Imran H. BiswasEmail author
  • Espen R. Jakobsen
  • Kenneth H. Karlsen
Article

Abstract

We develop a viscosity solution theory for a system of nonlinear degenerate parabolic integro-partial differential equations (IPDEs) related to stochastic optimal switching and control problems or stochastic games. In the case of stochastic optimal switching and control, we prove via dynamic programming methods that the value function is a viscosity solution of the IPDEs. In our setting the value functions or the solutions of the IPDEs are not smooth, so classical verification theorems do not apply.

Integro-partial differential equations Dynamic programming method Viscosity solutions Optimal stochastic control and switching Lévy processes 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Imran H. Biswas
    • 1
    Email author
  • Espen R. Jakobsen
    • 2
  • Kenneth H. Karlsen
    • 3
  1. 1.Seminar für Angewandte Mathematik, D-MATHETH-ZurichZurichSwitzerland
  2. 2.Norwegian University of Science and TechnologyTrondheimNorway
  3. 3.Centre of Mathematics for ApplicationsUniversity of OsloOsloNorway

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