  This paper examines a continuous time intertemporal consumption and portfolio
choice problem with a stochastic differential utility preference of Epstein-Zin
type for a robust investor, who worries about model misspecification and seeks
robust decision rules. We provide a verification theorem which formulates the
Hamilton-Jacobi-Bellman-Isaacs equation under a non-Lipschitz condition. Then,
with the verification theorem, the explicit closed-form optimal robust
consumption and portfolio solutions to a Heston model are given. Also we
compare our robust solutions with the non-robust ones, and the comparisons
shown in a few figures coincide with our common sense.
