Journal
ADVANCES IN APPLIED PROBABILITY
Volume 53, Issue 2, Pages 301-334Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/apr.2020.64
Keywords
Continuous-time Markov decision processes; dynamic programming; gradual-impulse control; optimality equation
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Funding
- Royal Society [IE160503]
- Daiwa Anglo-Japanese Foundation (UK) [4530/12801]
- EPSRC [EP/T018216/1, EP/I001328/1] Funding Source: UKRI
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This study investigates a gradual-impulse control problem of continuous-time Markov decision processes and demonstrates the existence of a deterministic stationary optimal policy under natural conditions, allowing multiple simultaneous impulses, randomized selection of impulses with random effects, and accumulation of jumps. The problem is simplified to an equivalent simple discrete-time Markov decision process, where the action space is the union of gradual and impulsive actions.
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.
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