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dc.contributor.authorFernandez-Tapia, Joaquin
dc.contributor.authorGuéant, Olivier
dc.contributor.authorLasry, Jean-Michel
dc.date.accessioned2019-02-28T15:16:37Z
dc.date.available2019-02-28T15:16:37Z
dc.date.issued2017
dc.identifier.issn1687-1200
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18501
dc.language.isoenen
dc.subjectReal-Time Biddingen
dc.subjectVickrey auctionsen
dc.subjectStochastic optimal controlen
dc.subjectConvex analysisen
dc.subjectFluid limit approximationen
dc.subject.ddc515en
dc.titleOptimal Real-Time Bidding Strategiesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe ad trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, real-time bidding algorithms respond to many auctions—usually Vickrey auctions—throughout the day for buying ad-inventory with the aim of maximizing one or several key performance indicators. The optimization problems faced by companies building bidding strategies are new and interesting for the community of applied mathematicians. In this article, we introduce a stochastic optimal control model that addresses the question of the optimal bidding strategy in various realistic contexts: the maximization of the inventory bought with a given amount of cash in the framework of audience strategies, the maximization of the number of conversions/acquisitions with a given amount of cash, etc. In our model, the sequence of auctions is modeled by a Poisson process and the price to beat for each auction is modeled by a random variable following almost any probability distribution. We show that the optimal bids are characterized by a Hamilton–Jacobi–Bellman equation, and that almost-closed-form solutions can be found by using a fluid limit. Numerical examples are also provided.en
dc.relation.isversionofjnlnameApplied Mathematics Research Express
dc.relation.isversionofjnlvolMarch 2017en
dc.relation.isversionofjnlissue1, 1en
dc.relation.isversionofjnldate2017-03
dc.relation.isversionofjnlpages142–183en
dc.relation.isversionofdoi10.1093/amrx/abw007en
dc.relation.isversionofjnlpublisherOxford University Pressen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-02-28T15:11:33Z
hal.person.labIds102
hal.person.labIds92774
hal.person.labIds60


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