期刊
ADVANCES IN APPLIED PROBABILITY
卷 53, 期 2, 页码 301-334出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/apr.2020.64
关键词
Continuous-time Markov decision processes; dynamic programming; gradual-impulse control; optimality equation
资金
- Royal Society [IE160503]
- Daiwa Anglo-Japanese Foundation (UK) [4530/12801]
- EPSRC [EP/T018216/1, EP/I001328/1] Funding Source: UKRI
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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