In an incomplete market we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein-Zin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton-Jacobi-Bellman equation and provide a suitable verification theorem....

We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic di erential utility, as introduced by Du e and Epstein (1992), in the continuous-time limit of vanishing grid size

We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Duffie and Epstein (1992), in the continuous-time limit of vanishing grid size.

We study consumption-portfolio and asset pricing frameworks with recursive preferences and unspanned risk. We show that in both cases, portfolio choice and asset pricing, the value function of the investor/representative agent can be characterized by a specific semilinear partial differential...

This paper relates recursive utility in continuous time to its discrete-time origins and provides a rigorous and intuitive alternative to a heuristic approach presented in [Duffie, Epstein 1992], who formally define recursive utility in continuous time via backward stochastic differential...