Approximate analytical solutions for consumption/investment problems under recursive utility and finite horizon

Résumé

We study the asset allocation and consumption decisions of an investor with recursive utility and a finite investment horizon. We provide an approximate analytical solution under a stochastic investment opportunity set. The solution becomes exact when the elasticity of intertemporal substitution is equal to one or under a constant opportunity set. We show that this elasticity impacts both consumption and portfolio strategies, indicating the importance of disentangling intertemporal substitution from risk aversion. The investor’s horizon also plays a crucial role in optimal policies and the usual infinite horizon framework is inappropriate for investors having short- or medium-term horizons. Moreover, the infinite horizon problem reveals the existence of conditions on the preference parameters for our solution to hold, raising the question of whether another solution may exist or not. On its turn, the absence of a bequest motive in the finite horizon problem imposes another condition on risk parameters.