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In a market with stochastic investment opportunities, we study an optimalconsumption investment problem for an agent with recursive utility ofEpstein-Zin type. Focusing on the empirically relevant specification where bothrisk aversion and elasticity of intertemporal substitution are in excess ofone, we characterize optimal consumption and investment strategies via backwardstochastic differential equations. The supperdifferential of indirect utilityis also obtained, meeting demands from applications in which Epstein-Zinutilities were used to resolve several asset pricing puzzles. The empiricallyrelevant utility specification introduces difficulties to the optimizationproblem due to the fact that the Epstein-Zin aggregator is neither Lipschitznor jointly concave in all its variables.

Consumption investment optimization with Epstein-Zin utility in incomplete markets