Ramaswamy, Mythily and Dharmatti, Sheetal (2006) Uniqueness of unbounded viscosity solutions for impulse control problem. In: Journal of Mathematical Analysis and Applications, 315 (2). pp. 686-710.
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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.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier.|
|Keywords:||Dynamic programming principle; Viscosity solution; Quasivariational inequality; Impulse control.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||04 Mar 2008|
|Last Modified:||19 Sep 2010 04:43|
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