  The paper investigates the consumption-investment problem for an investor
with Epstein-Zin utility in an incomplete market. A non-Markovian environment
with unbounded parameters is considered, which is more realistic in practical
financial scenarios compared to the Markovian setting. The optimal consumption
and investment strategies are derived using the martingale optimal principle
and quadratic backward stochastic differential equations (BSDEs) whose
solutions admit some exponential moment. This integrability property plays a
crucial role in establishing a key martingale argument. In addition, the paper
also examines the associated dual problem and several models within the
specified parameter framework.
