Uniqueness of unbounded viscosity solutions for impulse control problem |
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Authors: | Mythily Ramaswamy Sheetal Dharmatti |
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Institution: | a IISc-TIFR Mathematics Program, TIFR Center, PO Box 1234, Bangalore 560012, India b Department of Mathematics, Indian Institute of Science, Bangalore 560012, India |
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Abstract: | We study here the impulse control problem in infinite as well as finite horizon. We allow the cost functionals and dynamics to be unbounded and hence the value function can possibly be unbounded. We prove that the value function is the unique viscosity solution in a suitable subclass of continuous functions, of the associated quasivariational inequality. Our uniqueness proof for the infinite horizon problem uses stopping time problem and for the finite horizon problem, comparison method. However, we assume proper growth conditions on the cost functionals and the dynamics. |
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Keywords: | Dynamic programming principle Viscosity solution Quasivariational inequality Impulse control |
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