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

本文的目的是详细介绍具有 Epstein-Zin (EZ) 随机微分效用 (SDU) 描述的偏好的代理人的无限期投资-消费问题。在 Black-Scholes-Merton 市场的背景下，我们试图描述所有导致有充分根据的问题的参数组合，因为这个问题不仅在数学上是恰当的，而且解决方案在经济上也有意义。关键思想是考虑一种新颖且略有不同的 EZ SDU 描述，在该描述下聚合器只有一个符号。这个新公式清楚地强调了相对风险厌恶系数和跨期互补弹性系数（跨期替代系数的倒数）位于统一的同一侧的必要性。