Robust utility maximization problem in model with jumps and unbounded   claim
  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. 
Monique Jeanblanc, Anis Matoussi, and Armand Ngoupeyou
math.PR