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

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2021

Xin Guo ,
Aiko Kurushima ,
Alexey Piunovskiy  and
Yi Zhang
Xin Guo*
Affiliation:
Tsinghua University
Aiko Kurushima*
Affiliation:
Sophia University
Alexey Piunovskiy*
Affiliation:
University of Liverpool
Yi Zhang*
Affiliation:
University of Liverpool
*
*Postal address: School of Economics and Management, Tsinghua University, Beijing 100084, China. Email address: guoxin5@sem.tsinghua.edu.cn
**Postal address: Department of Economics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo, 102-8554, Japan. Email address: kurushima@sophia.ac.jp
***Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK.
***Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK.
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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.

Keywords

Continuous-time Markov decision processesdynamic programminggradual-impulse controloptimality equation

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60J75: Jump processes
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 2 , June 2021 , pp. 301 - 334
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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