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

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-009-9095-8· OSTI ID:21480261

Biswas, Imran H., E-mail: [e-mail].c ^[1]; Jakobsen, Espen R., E-mail: [e-mail].n ^[2]; Karlsen, Kenneth H., E-mail: [e-mail].n ^[3]

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1. ETH-Zurich, Seminar fuer Angewandte Mathematik, D-MATH (Switzerland)
2. Norwegian University of Science and Technology (Norway)
3. University of Oslo, Centre of Mathematics for Applications (Norway)

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.

• OSTI ID: 21480261
• Journal Information: Applied Mathematics and Optimization, Vol. 62, Issue 1; Other Information: DOI: 10.1007/s00245-009-9095-8; Copyright (c) 2010 Springer Science+Business Media, LLC; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CONTROL THEORY
DYNAMIC PROGRAMMING
FUNCTIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES
VERIFICATION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS