  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 continuoustime
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.

Optimization and Control;Computational Finance