Before revision:  Focusing on the empirically relevant specification where both the risk aversion and the elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations.
After revision:  Focusing on the empirically relevant specification where both risk aversion and the elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations.