  In this article we consider the optimal investment-consumption problem for an
agent with preferences governed by Epstein-Zin stochastic differential utility
who invests in a constant-parameter Black-Scholes-Merton market.
  The paper has three main goals: first, to provide a detailed introduction to
infinite-horizon Epstein-Zin stochastic differential utility, including a
discussion of which parameter combinations lead to a well-formulated problem;
second, to prove existence and uniqueness of infinite horizon Epstein-Zin
stochastic differential utility under a restriction on the parameters governing
the agent's risk aversion and temporal variance aversion; and third, to provide
a verification argument for the candidate optimal solution to the
investment-consumption problem among all admissible consumption streams.
  To achieve these goals, we introduce a slightly different formulation of
Epstein-Zin stochastic differential utility to that which is traditionally used
in the literature. This formulation highlights the necessity and
appropriateness of certain restrictions on the parameters governing the
stochastic differential utility function.
