Laboratoire Manceau
de Mathématiques
Equipe d'Accueil N° 3263
Membre de la Fédération de mathématiques des Pays de Loire
Faculté des Sciences et Techniques - Université du Maine
MU Rui
Anciens doctorants AUBRY Christophe BACHOUCH Achref BEN ABDEDDAIEM Maroua CAI Chunhao DABYE Ali S. DACHIAN Sergueï DALALYAN Arnak ELSARI Brahim FAZLI Khosrow GASSEM Anis HDHIRI Ibtissam KABUI Ali M. LACUS Stefano MOTRUNICH Anastasiia MU Rui NEGRI Ilia PIOZIN Lambert SABBAGH Wissal SAUSSEREAU Bruno WANG Hao XU Mingyu YANG Lin ZHAO Xuzhe ZHOU Li

Sujet de thèse (Soutenue le 26 Septembre 2014 ) :

- Jeux Différentiels Stochastiques de Somme Non Nulle et Equations Différentielles Stochastiques Rétrogrades Multidimensionnelles

Directeur de thèse : Prof. S. HAMADENE

- Télécharger la thèse sous forme de : Fichier PDF

Résumé :

This dissertation studies the multiple players nonzero-sum stochastic differential games (NZSDG) in the Markovian framework and their connections with multiple dimensional backward stochastic differential equations (BSDEs). There are three problems that we are focused on. Firstly, we consider a NZSDG where the drift coefficient is not bound but is of linear growth. Some particular cases of unbounded diffusion coefficient of the diffusion process are also considered. The existence of Nash equilibrium point is proved under the generalized Isaacs condition via the existence of the solution of the associated BSDE. The novelty is that the generator of the BSDE is multiple dimensional, continuous and of stochastic linear growth with respect to the volatility process. The second problem is of risk-sensitive type, i.e. the payoffs integrate utility exponential functions, and the drift of the diffusion is unbounded. The associated BSDE is of multi-dimension whose generator is quadratic on the volatility. Once again we show the existence of Nash equilibria via the solution of the BSDE. The last problem that we treat is a bang-bang game which leads to discontinuous Hamiltonians. We reformulate the verification theorem and we show the existence of a Nash point for the game which is of bang-bang type, i.e., it takes its values in the border of the domain according to the sign of the derivatives of the value function. The BSDE in this case is a coupled multi-dimensional system, whose generator is discontinuous on the volatility process.

 
 
Mise à jour 2014 I.Croset

Laboratoire Manceau de Mathématiques
Université du Maine - Faculté des Sciences et Techniques
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