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On stochastic control under poissonian intervention: optimality of a barrier strategy in a general Lévy model

Part of: Operations research and management science Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  09 January 2025

Kei Noba Open the ORCID record for Kei Noba [Opens in a new window]  and
Kazutoshi Yamazaki Open the ORCID record for Kazutoshi Yamazaki [Opens in a new window]
Kei Noba*
Affiliation:
The Institute of Statistical Mathematics
Kazutoshi Yamazaki*
Affiliation:
The University of Queensland
*
*Postal address: Department of Fundamental Statistical Mathematics, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa-shi, Tokyo 190-8562, Japan. Email address: [email protected]
**Postal address: School of Mathematics and Physics, The University of Queensland, St Lucia, Brisbane, QLD 4072, Australia. Email address: [email protected]
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Abstract

We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general Lévy process, we show the optimality of a periodic barrier strategy, which moves the process upward to the barrier whenever it is observed to be below it. The convergence of the optimal solutions to those in the continuous-observation case is also shown.

Keywords

Stochastic controlinventory modelsperiodic observationsmathematical financeLévy processes

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 93E20: Optimal stochastic control 90B05: Inventory, storage, reservoirs
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 24
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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