Stochastic control and mean-field games
In this mini-course we will give a short introduction of stochastic control problems and
games, especially in view to applications in economics and finance such as - but not limited
to - portfolio optimization. Two main approaches will be discussed: dynamic programming
principle via PDEs (Partial Differential Equations), Pontryagin maximum principle via
BSDEs (Backward Stochastic Differential Equations). Moreover, an application to the
latter method to the very popular class of mean-field games (MFGs) will be presented as
well together with some relevant applications to study strategic interaction among economic
agents, such as banks and investors. Other applications of MFGs to, for instance, energy
markets and crowd dynamics, will be also discussed if time allows.
The list of topics will be:
(i) Stochastic control: formulation of the problem with examples.
(ii) Dynamic programming principle and Hamilton-Jacobi-Bellman PDE.
(iii) Pontryagin stochastic maximum principle and BSDEs.
(iv) Mean-field games: characterization of Nash equilibria and applications.
• Carmona, R., Delarue, F. (2018). Probabilistic Theory of Mean Field Games with
Applications I-II. Springer Nature.
• Pham, H. (2009). Continuous-time stochastic control and optimization with financial
applications (Vol. 61). Springer Science & Business Media.
• Touzi, N. (2012). Optimal stochastic control, stochastic target problems, and back-
ward SDE (Vol. 29). Springer Science & Business Media.
Other more specific references will be given during the lectures when needed.
Monday, 29th of April: 16.30 18.30 [ Room M ]
Tuesday 30th of April: 12.30 -15.30 [ seminar room, entrance, Ca' Vignal 1 ]
Thursday, 2nd of May: 12.30 -15.30 [ Room M ]
Strada le Grazie 15
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Italian Fiscal Code 93009870234
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