We also study the corresponding Mean Field Game in the limit of large number of banks in the presence of a common noise.doi:10.2139/ssrn.2307814Rene CarmonaJean-Pierre FouqueLi-Hsien SunarXiv.orgPapersCarmona, R., Fouque, J.P., Sun, L.H.: Mean field games and systemic risk. arXiv:...
In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii) systemic risk induced through inter-bank lending/borrowing....
Mathieu Lauriere and Olivier Pironneau. Dynamic programming for mean-field type control. Comptes Rendus Mathematique, 352(9):707-713, 2014.Lauri`ere M. and O. Pironneau (2014): "Dynamic programming for mean-field type control", CRAS, 352(9), 707-713....
To capture the essence of such problems, here, we introduce a general class of non-cooperative heterogeneous stochastic games with one major agent and a large population of minor agents where agents interact with an observed common process impacted by the mean field. A latent Markov chain and a...
We give explicit solutions to the Bellman equation for the linear quadratic mean-field control problem, with applications to the mean-variance portfolio selection and a systemic risk model. We also consider a notion of lifted visc-sity solutions for the Bellman equation, and show the viscosity ...
We formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise, including a rigorous pro
Mean field game (MFG) theory studies the existence of Nash equilibria, together with the individual strategies which generate them, in games involving a large number of asymptotically negligible agents modeled by controlled stochastic dynamical systems. This is achieved by exploiting the relationship betw...
We also\nstudy the corresponding Mean Field Game in the limit of large number of banks\nin the presence of a common noise.doi:10.2139/SSRN.2307814Rene CarmonaJean-Pierre FouqueLi-Hsien SunarXiv.orgRene Carmona, Jean-Pierre Fouque, and Li-Hsien Sun. Mean field games and systemic risk. ...
: Mean-field games and systemic risk. Communications in Math- ematical Sciences, Vol. 13(4), p. 911-933 (2015)Carmona R., Fouque J.P. and L. Sun (2015): "Mean field games and systemic risk", Commu- nications in Mathematical Sciences, 13(4), 911-933....
Lions' analysis of mean-field games (2007) [10]. We derive HJB equations and apply them to two examples, a portfolio optimization and a systemic risk model. Résumé Pour les problèmes de contrôle stochastique à champs moyen, la programmation dynamique ne s'applique pas sans adaptation ...