Consider a publisher of online display advertising that sells its ad resources in both an upfront market and a spot market. When planning its ad delivery, the publisher needs to make a trade-off between earning a greater short-term profit from the spot market and improving advertising...

This paper considers an optimal control problem for the dynamics of the Nerlove-­Arrow advertising model, the optimal control being the rate of advertising expenditure required to maximize the present value of net profit streams (or, sales) over a finite horizon subject to a budget constraint....