Viscosity Solutions of Path-Dependent PDEs

Path-dependent parabolic second order PDEs aim at extending the standard corresponding PDE tools to non-Markovian phenomena, where the function of interest is a stochastic process depending at each point in time on the current history. Applications include stochastic control of non-Markovian stochastic systems and the corresponding stochastic differential games. Similar to the PDE theory, we introduce a notion of viscosity solutions which by-passes the local compactness of the underlying space. Our objective is to review the recent developments on the wellposedness of these equations.

Location:
Speaker(s):

Nizar Touzi, Centre de Mathématiques Appliquées Ecole Polytechnique (CMAP)

Start date:
Monday, October 20, 2014 - 09:00
End date:
Tuesday, October 21, 2014 - 12:00