# Mean-field stochastic differential equation

Tuesday, June 12, 2018 - 9:00am - 9:50am

Bernt Oksendal (University of Oslo)

We consider the problem of optimal control of a mean-field stochastic differential equation (SDE) under model uncertainty. The model uncertainty is represented by ambiguity about the law L(X(t)) of the state X(t) at time t. For example, it could be the law L_P(X(t)) of X(t) with respect to the given, underlying probability measure P. This is the classical case when there is no model uncertainty. But it could also be the law L_Q(X(t)) with respect to some other probability measure Q or, more generally, any random measure \mu(t) on R with total mass 1.