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

Biswas, Imran ; Jakobsen, Espen ; Karlsen, Kenneth

In: Applied Mathematics and Optimization, 2010, vol. 62, no. 1, p. 47-80

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    Titre
    • Viscosity Solutions for a System of Integro-PDEs andConnections to Optimal Switching and Control ofJump-Diffusion Processes
    Auteur
    • Biswas, Imran. Seminar für Angewandte Mathematik, D-MATH, ETH-Zurich, HG G 56.2, Rämistrasse 101, 8092, Zurich, Switzerland
    • Jakobsen, Espen. Norwegian University of Science and Technology, 7491, Trondheim, Norway
    • Karlsen, Kenneth. Centre of Mathematics for Applications, University of Oslo, Blindern, P.O. Box 1053, 0316, Oslo, Norway
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Applied Mathematics and Optimization, 2010, vol. 62, no. 1, p. 47-80. Springer-Verlag
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:321893
    Summary
    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