Optimal stochastic control of the intensity of point processes

초록

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 Bremaud (1976) and Defourny (2018). Also, we resolve the two conjectures made by Defourny (2018).(c) 2022 Elsevier B.V. All rights reserved.

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