Optimal bidding strategies for digital advertising with social interactions


With the emergence of new online channels and information technology, digital advertising tends to substitute more and more to traditional advertising by offering the opportunity to companies to target the consumers/users that are really interested by their products or services. We introduce a novel framework for the study of optimal bidding strategies associated to different types of advertising, namely, commercial advertising for triggering purchases or subscriptions, and social marketing for alerting population about unhealthy behaviours (anti-drug, vaccination, road-safety campaigns). Our continuous-time models are based on a common framework encoding users online behaviours via their web-browsing at random times, and the targeted advertising auction mechanism widely used on Internet, the objective being to efficiently diffuse advertising information by means of digital channels. Our main results are to provide semi-explicit formulas for the optimal value and bidding policy for each of these problems.

We show some sensitivity properties of the solution with respect to model parameters, and analyse how the different sources of digital information accessible to users including the social interactions affect the optimal bid for advertising auctions. We also study how to efficiently combine targeted advertising and non-targeted advertising mechanisms. Finally, some classes of examples with fully explicit formulas are derived.


Huyên PHAM is Distinguished Professor of Mathematics at Université de Paris, and adjunct Professor at ENSAE.  He leads research in quantitative finance, stochastic analysis and control, machine learning techniques for numerical probabilities, and is the author of more than 100 publications, including the monograph Continuous time Stochastic Control and Optimization with Financial Applications. He serves on the editorial boards of several international journals, and is the co-editor in chief of the journal Applied Mathematics and Optimization. Prof. Pham was appointed member of the Institut Universitaire de France in 2006, awarded the Louis Bachelier prize by the French Academy of Sciences in 2007, and was a plenary speaker at the 9th World congress of the Bachelier Finance Society in 2016, and at the 6th Asian Quantitative Finance Conference in 2018.  


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