Robust utility maximization with a general penalty term

Wahid Faidi, Anis Matoussi, Mohamed Mnif

Published 2013-02-03, updated 2015-09-18Version 4

In this paper, a robust stochastic control problem with general penalty term is studied in the dominated case. Two types of penalties are considered. The first one is of type f-divergence penalty treated in the general framework of a continuous filtration. The second one called consistent time penalty studied in the context of a Brownian filtration. Existence and uniqueness of the optimal model of the robust problem are proved. Moreover, the optimal model is equivalent to the reference probability measure. In the case of consistent time penalty, we characterize the dynamic value process of our stochastic control problem as the unique solution of a class of quadratic backward stochastic differential equation with unbounbed terminal condition.