Optimality of an affine intensity policy for maximizing the probability of an arrival count in point-process intensity control

摘要

This paper considers the problem of maximizing the probability of attaining a prescribed count of arrivals generated by a point process, by controlling its intensity. Our analysis shows the existence of optimal intensity switching times that are affine in the arrival count, thereby contributing to the literature on the optimality of affine policies. The optimal intensity control law is established, along with closed-form expressions for its numerical parameters. Several properties of the value function are listed as well. (C) 2017 Elsevier B.V. All rights reserved.