Boundary value problems for stochastic budget distribution in search advertisements

In sponsored search auctions, advertisers have to distribute the budget to a series of temporal slots in order to maximize the expected revenue. There exists a budget demand for each temporal slot, which can not be known exactly by the advertiser due to some uncertainties in the search marketing environments. The estimation of the value range of budget demand in a temporal slot seriously affects the advertising performance. In this paper we study the effect of the value range on the revenue and conduct some experiments to validate our model and identified properties with the real-world data collected from practical advertising campaigns. Experimental results show that, under a certain condition, (a) the higher estimation of the upper bound and the lower bound might increase the expected revenue, and (b) the expected revenue is positively proportional to the mean value of the value range and is negatively proportional to the size.