Quelques problèmes de transport et de contrôle en économie: aspects théoriques et numériques
AbstractIn this thesis we explore some uses of optimal control and mass transport in economic modeling. We thus catch the opportunity to bring together some works involving both tools, sometimes mixing them. First, we brieﬂy present the recent mean field games theory introduced by Lasry & Lions and focus on the optimal control of Fokker-Planck setting. We take advantage of this aspect in order to obtain both existence results and numerical methods to approximate solutions. We test the algorithms on two complementary settings, namely the convex setting (crowd aversion, two populations dynamics) and the concave one (attraction, externalities and scale effect for a stylized technology switch model). Secondly, we study matching problems combining optimal transport and optimal control. The planner looks for an optimal coupling, ﬁxed during the considered time period (commitment), knowing that the marginals evolve (possibly randomly) and that she can control the evolution. Finally we reformulate a risk-sharing problem between d agents (for whose we prove an existence result) into an optimal control problem with comonotonic constraints. This enables us to write optimality conditions that we use to build a simple convergent algorithm.
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Bibliographic InfoThis book is provided by Paris Dauphine University in its series Economics Thesis from University Paris Dauphine with number 123456789/5226 and published in 2010.
Jeux à champ moyen; calculus of variations; Fokker-Planck control; mathematical economics; contrôle optimal; transport optimal; approximations numériques; calcul des variations; contrôle de Fokker-Planck; économie mathématique; Mean ﬁeld games; optimal control; optimal transport; numerical approximations;
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- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
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