The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. I: Foundations

Abstract The goal of this article is to provide a detailed introduction infinite-horizon investment–consumption problems for agents with preferences described by Epstein–Zin (EZ) stochastic differential utility (SDU). In the setting Black–Scholes–Merton market, we seek describe all parameter combinations that lead well-founded problem in sense not just mathematically well posed, but solution also economically meaningful. key idea consider novel and slightly different description EZ SDU under which aggregator has only one sign. This new formulation clearly highlights necessity coefficients relative risk aversion elasticity intertemporal complementarity (the reciprocal coefficient substitution) lie on same side unity.