Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem

This paper deals with existence and uniqueness of a solution in viscosity sense, for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case is the Hamilton-Jacobi-Bellmann system of the Markovian stochastic optimal m -states switching problem. T...

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Bibliographic Details
Published in:Applied mathematics & optimization 2013-04, Vol.67 (2), p.163-196
Main Authors: Hamadène, S., Morlais, M. A.
Format: Article
Language:English
Subjects:
Applied mathematics
Calculus of Variations and Optimal Control
Optimization
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Control
COST
Costs
Differential equations
FUNCTIONS
HAMILTON-JACOBI EQUATIONS
MARKOV PROCESS
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
MATHEMATICAL SOLUTIONS
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Obstacles
Optimization
Optimization and Control
Partial differential equations
Probability
Random variables
Real options analysis
REFLECTION
Simulation
Stochasticity
Studies
Switching
Systems Theory
Theoretical
VARIATIONAL METHODS
VISCOSITY
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Summary:This paper deals with existence and uniqueness of a solution in viscosity sense, for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case is the Hamilton-Jacobi-Bellmann system of the Markovian stochastic optimal m -states switching problem. The switching cost functions depend on ( t , x ). The main tool is the notion of systems of reflected backward stochastic differential equations with oblique reflection.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-012-9184-y