Abstract

This paper establishes existence of optimal controls for a general stochastic impulse control problem. For this, the value function is characterized as the pointwise minimum of a set of superharmonic functions, as the unique continuous viscosity solution of the quasi-variational inequalities (QVIs), and as the limit of a sequence of iterated optimal stopping problems. A combination of these characterizations is used to construct optimal controls without relying on any regularity of the value function beyond continuity. Our approach is based on the stochastic Perron method and the assumption that the associated QVIs satisfy a comparison principle.

Keywords

  1. impulse control
  2. stochastic Perron
  3. superharmonic functions
  4. optimal controls

MSC codes

  1. 93E20
  2. 49L25
  3. 60J60
  4. 60J45

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Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 627 - 649
ISSN (online): 1095-7138

History

Submitted: 5 July 2016
Accepted: 7 December 2016
Published online: 2 March 2017

Keywords

  1. impulse control
  2. stochastic Perron
  3. superharmonic functions
  4. optimal controls

MSC codes

  1. 93E20
  2. 49L25
  3. 60J60
  4. 60J45

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