The Dept. of Comp. Science, College of Mathematics [ UniVr ] :

https://goo.gl/maps/yeKWo3vri8PkHjUm9

will host the following mini-course

*Title*: Stochastic control and mean-field games [ 2 ECTS ]

which will be given by prof. Luciano Campi [LSE - London]

*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.

*Main references*: • 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.

*Time-table*

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 ]

See also: http://www.di.univr.it/?ent=seminario&id=4706

Do not hesitate to contact me: luca.dipersio@univr.it for any further info.

Best, LuCa

__ Luca Di Persio - PhD College of Mathematics Dept. of Computer Science - University of Verona strada le Grazie 15 - 37134 Verona - Italy Tel : +39 045 802 7968

http://www.hpa8.com/