  In this paper, we consider a dynamic coalition portfolio selection problem,
with each agent's objective given by an Epstein--Zin recursive utility. To find
a Pareto optimum, the coalition's problem is formulated as an optimization
problem evolved by a multi-dimensional forward-backward SDE. Since the
evolution system has a forward-backward structure, the problem is intrinsically
time-inconsistent. With the dynamic-game point of view, we rigorously develop
an approach to finding the equilibrium Pareto investment-consumption strategy.
We find that the relationship between risk aversion and EIS has more influence
on the coalition's problem than that on the one-agent problem. More
interestingly, we show that the equilibrium Pareto consumption strategy
associated with the recursive utility is much more effective than that
associated with the CRRA expected utility, which highlights the feature of
recursive utilities that the marginal benefit of consumption can depend on the
future consumption.
