On gradual-impulse control of continuous-time Markov decision processes with exponential utility

Xin Guo, Aiko Kurushima, Alexey Piunovskiy, Yi Zhang

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Abstract

We consider a gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We show, under natural conditions on the system primitives, the existence of a deterministic stationary optimal policy out of a more general class of policies that allow multiple simultaneous impulses, randomized selection of impulses with random effects, and accumulation of jumps. After characterizing the value function using the optimality equation, we reduce the gradual-impulse control problem to an equivalent simple discrete-time Markov decision process, whose action space is the union of the sets of gradual and impulsive actions.
Original languageEnglish
Pages (from-to)301-334
Number of pages34
JournalAdvances in Applied Probability
Volume53
Issue number2
DOIs
Publication statusPublished - 1 Jul 2021

Keywords

  • Continuous-time Markov decision processes
  • dynamic programming
  • gradual-impulse control
  • optimality equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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