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В субботу состоится совместное заседание Глобального семинара по финансовой математике и Межкафедрального научно-исследовательского семинара по Экономике и Математическим методам.

Sergey A. Vartanov, assistant professor, Economic and Financial Strategy Department, MSE MSU

Topic: The Stochastic control problems for modelling advertising dynamics: the state-of-the-art overview

Abstract: Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we discuss two basic groups of models (both deterministic and stochastic), corresponding to the type of primary advertisement influence on the customers. The first one describes models of short-time persuasion, which are similar to (and loosely based on) the well-known Vidale-Wolfe model. Another group of models deals with long-time persuasion and prestige effects and is based on different (stochastic or deterministic) perturbations of the classical Nerlove-Arrow dynamics.
There are different goals and formulations of the key problems-to-be solved in this area. First is to determine the optimal strategies for the problem of maximizing the utility of a firm at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for the considered models. We also consider some generalizations such as problems with constrained budget and with discretionary launching as well as problems with two and more firms. The latter are solved using differential game-theoretic concepts like open- and closed-loop Nash equilibria.

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