  We study a problem of utility maximization under model uncertainty with
information including jumps. We prove first that the value process of the
robust stochastic control problem is described by the solution of a
quadratic-exponential backward stochastic differential equation with jumps.
Then, we establish a dynamic maximum principle for the optimal control of the
maximization problem. The characterization of the optimal model and the optimal
control (consumption-investment) is given via a forward-backward system which
generalizes the result of Duffie and Skiadas (1994) and El Karoui, Peng and
Quenez (2001) in the case of maximization of recursive utilities including
model with jumps.
