Dynamic Programming with Recursive Preferences: Optimality and Applications

TL;DR

This paper develops new conditions for dynamic optimality in discrete time, enabling the analysis of various recursive preferences and providing foundational results for optimal policies and computational methods.

Contribution

It introduces novel conditions for dynamic optimality applicable to multiple recursive preference models, establishing existence, uniqueness, and computational methods.

Findings

Existence of optimal policies for recursive preferences

Uniqueness of solutions to Bellman equations

Globally convergent value function iteration method

Abstract

This paper provides new conditions for dynamic optimality in discrete time and uses them to establish fundamental dynamic programming results for several commonly used recursive preference specifications. These include Epstein-Zin preferences, risk-sensitive preferences, narrow framing models and recursive preferences with sensitivity to ambiguity. The results obtained for these applications include (i) existence of optimal policies, (ii) uniqueness of solutions to the Bellman equation, (iii) a complete characterization of optimal policies via Bellman's principle of optimality, and (iv) a globally convergent method of computation via value function iteration.