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

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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.

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Authors and Affiliations

  1. Seminar für Angewandte Mathematik, D-MATH, ETH-Zurich, HG G 56.2, Rämistrasse 101, 8092, Zurich, Switzerland

    Imran H. Biswas

  2. Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Espen R. Jakobsen

  3. Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway

    Kenneth H. Karlsen

Authors
  1. Imran H. Biswas
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  2. Espen R. Jakobsen
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  3. Kenneth H. Karlsen
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Correspondence to Imran H. Biswas.

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Communicating Editor: Frederic Bonnans.

This research is supported by the Research Council of Norway through an Outstanding Young Investigators Award (KHK) and partially through the project “Integro-PDEs: Numerical methods, Analysis, and Applications to Finance”.

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Biswas, I.H., Jakobsen, E.R. & Karlsen, K.H. Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes. Appl Math Optim 62, 47–80 (2010). https://doi.org/10.1007/s00245-009-9095-8

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