Existence and uniqueness of recursive utilities without boundedness

TL;DR

This paper establishes simple, verifiable conditions for the existence and uniqueness of recursive utilities in models with unbounded state spaces and utilities, covering various preference classes including Epstein-Zin and ambiguity models.

Contribution

It introduces primitive 'thin tail' conditions that ensure existence and uniqueness of recursive utilities in unbounded settings, broadening applicability.

Findings

Existence and uniqueness under 'thin tail' conditions

Applicable to models with unbounded utilities and state spaces

Includes applications to robust preferences and Epstein-Zin models

Abstract

This paper derives primitive, easily verifiable sufficient conditions for existence and uniqueness of (stochastic) recursive utilities for several important classes of preferences. In order to accommodate models commonly used in practice, we allow both the state-space and per-period utilities to be unbounded. For many of the models we study, existence and uniqueness is established under a single, primitive "thin tail" condition on the distribution of growth in per-period utilities. We present several applications to robust preferences, models of ambiguity aversion and learning about hidden states, and Epstein-Zin preferences.