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).
Bibliographical noteFunding 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 ).
© 2022 Elsevier B.V.
- Intensity control
- Point process
ASJC Scopus subject areas
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics