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

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 program...

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Bibliographic Details
Published in:Applied mathematics & optimization 2010-08, Vol.62 (1), p.47-80
Main Authors: Biswas, Imran H., Jakobsen, Espen R., Karlsen, Kenneth H.
Format: Article
Language:English
Subjects:
Approximation
CALCULATION METHODS
Calculus of Variations and Optimal Control
Optimization
Control
CONTROL THEORY
DIFFERENTIAL EQUATIONS
Diffusion
DYNAMIC PROGRAMMING
EQUATIONS
FUNCTIONS
Mathematical and Computational Physics
Mathematical functions
MATHEMATICAL METHODS AND COMPUTING
Mathematical Methods in Physics
MATHEMATICAL SOLUTIONS
Mathematics
Mathematics and Statistics
NONLINEAR PROBLEMS
Numerical and Computational Physics
PARTIAL DIFFERENTIAL EQUATIONS
Production planning
Simulation
Stochastic models
STOCHASTIC PROCESSES
Studies
Systems Theory
Theoretical
VERIFICATION
Viscosity
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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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-009-9095-8