On the Theory of Continuous-Time Recursive Utility

Abstract

We establish a connection between continuous-time recursive utility and the notion of consistency studied, in particular, in connection with the non-linear objective mean-variance. We propose a time-global optimization problem and show that the optimal time-consistent solution to this time-global problem is closely related to the standard recursive utility solution which is defined via differential equations. The two approaches are, to some extent, equivalent. Standard continuous-time recursive utility was developed for Brownain markets, and a generalization is complicated. Our approach contributes with insight in the notion of recursive utility and lightens up a relatively simple path that potentially gives access to results for general Markovian markets.

Keywords: Consistency, stochastic differential utility, pseudo-Bellman equations, time-globality, linear homogeneity

JEL Classification: C61, D91, G11