Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions

This paper examines an Epstein–Zin recursive utility with quasi-hyperbolic discounting in continuous time. I directly define the utility process supporting the Hamilton–Jacobi–Bellman (HJB) equation in the literature and consider Merton's optimal consumption–investment problem for application. I show that a solution to the HJB equation is the value function. The numerical and mathematical analyses show that unlike in the constant relative risk aversion utility, present bias in the Epstein–Zin utility causes economically significant overconsumption, maintaining a plausible attitude toward risks. Additionally, the sophisticated agent's preproperation occurs if and only if the elasticity of intertemporal substitution is larger than one.