Optimal stochastic control of the intensity of point processes

Bara Kim; Jeongsim Kim; Chia Li Wang

doi:10.1016/j.orl.2022.08.006

Optimal stochastic control of the intensity of point processes

Bara Kim, Jeongsim Kim, Chia Li Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an intensity control problem for a point process to maximize the expectation of a function of the time when the nth event occurs. We find the optimal control policy when the objective function is unimodal. Moreover, if the objective function is log-concave, so is the value function. As an application, we completely solve an intensity control problem that generalizes the problem studied by Brémaud (1976) and Defourny (2018). Also, we resolve the two conjectures made by Defourny (2018).

Original language	English
Pages (from-to)	574-580
Number of pages	7
Journal	Operations Research Letters
Volume	50
Issue number	5
DOIs	https://doi.org/10.1016/j.orl.2022.08.006
Publication status	Published - 2022 Sep

Keywords

Intensity control
Log-concavity
Point process

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2022.08.006

Cite this

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title = "Optimal stochastic control of the intensity of point processes",

abstract = "We consider an intensity control problem for a point process to maximize the expectation of a function of the time when the nth event occurs. We find the optimal control policy when the objective function is unimodal. Moreover, if the objective function is log-concave, so is the value function. As an application, we completely solve an intensity control problem that generalizes the problem studied by Br{\'e}maud (1976) and Defourny (2018). Also, we resolve the two conjectures made by Defourny (2018).",

keywords = "Intensity control, Log-concavity, Point process",

author = "Bara Kim and Jeongsim Kim and Wang, {Chia Li}",

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AU - Kim, Bara

AU - Kim, Jeongsim

AU - Wang, Chia Li

N1 - Funding Information: We are grateful to the Associate Editor and the reviewer for their valuable comments and suggestions. This work was supported under the framework of international cooperation program managed by the National Research Foundation of Korea ( 2019K2A9A1A06102882 , FY2019) and the Ministry of Science and Technology of Taiwan ( MOST-109-2923-H-259-001-MY2 ). Publisher Copyright: © 2022 Elsevier B.V.

PY - 2022/9

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N2 - We consider an intensity control problem for a point process to maximize the expectation of a function of the time when the nth event occurs. We find the optimal control policy when the objective function is unimodal. Moreover, if the objective function is log-concave, so is the value function. As an application, we completely solve an intensity control problem that generalizes the problem studied by Brémaud (1976) and Defourny (2018). Also, we resolve the two conjectures made by Defourny (2018).

AB - We consider an intensity control problem for a point process to maximize the expectation of a function of the time when the nth event occurs. We find the optimal control policy when the objective function is unimodal. Moreover, if the objective function is log-concave, so is the value function. As an application, we completely solve an intensity control problem that generalizes the problem studied by Brémaud (1976) and Defourny (2018). Also, we resolve the two conjectures made by Defourny (2018).

KW - Intensity control

KW - Log-concavity

KW - Point process

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M3 - Article

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VL - 50

SP - 574

EP - 580

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 5

ER -

Optimal stochastic control of the intensity of point processes

Abstract

Keywords

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